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Matt Higgins, a former judge on the reality TV show “Shark Tank,” is an experienced investor whose firm, RSE Ventures, helps young companies build their businesses.

So it was no surprise that in November 2020, Mr. Higgins embraced one of Wall Street’s biggest recent obsessions by launching a SPAC. Special purpose acquisition companies — known by their acronym — are shell entities that sell shares to the public and use those funds to buy an operating business. Investors get their money back if the SPAC hasn’t found a business to buy within a two-year window.

Last summer, Omnichannel Acquisition, the SPAC backed by Mr. Higgins, agreed to buy Kin Insurance, a fintech company. But in January, the two sides called off the deal, citing “unfavorable market conditions.” In May, Mr. Higgins decided he’d had enough. He is liquidating Omnichannel and returning the $206 million his SPAC raised to investors.

“We did months and months of work to get Kin ready to go,” Mr. Higgins said. “But the market completely turned on us.”

Wall Street’s love affair with SPACs is sputtering.

After two hot and heavy years, during which investors poured $250 billion into SPACs, rising inflation, interest rate increases and the threat of a recession are fomenting doubts. Increasingly, investors are withdrawing their money from SPACs, which they’re allowed to do at the time of the merger. With stocks of high-growth companies recently getting clobbered, they have been less willing to bet that SPAC mergers — which often involve risky companies — will be successful.

At the same time, regulators are stepping up scrutiny of SPACs. The Securities and Exchange Commission has opened dozens of investigations into SPACs and is proposing tighter rules. Increased regulation would make SPAC deals less profitable for the big investment banks that arrange these transactions, because they would have to commit more resources to comply. They, too, have begun pulling back.

“You could see this cliff coming,” said Usha Rodrigues, a professor of corporate law at the University of Georgia School of Law who has emerged as a leading expert on SPACs.

The wreckage is piling up.

On Tuesday, Forbes Media became the latest company to scrap its planned merger with a SPAC. Around 600 SPACs that went public in the past couple of years are still trying to complete deals, according to data from Dealogic. Roughly half of them might not find targets before their two-year window closes. At least seven SPACs have folded since the beginning of the year. Another 73 SPACs that were waiting to go public have shelved their plans. A fund that tracks the performance of 400 SPACs is down 40 percent over the past year.

Although SPACs had been around for decades, they long had an unsavory reputation. Only companies whose financials wouldn’t survive investor scrutiny en route to a traditional initial public offering used SPACs to go public. That changed at the beginning of 2020, when prominent financial firms, venture capitalists and hot start-ups embraced SPACs as a faster and easier route to the public markets than an I.P.O.

Wall Street banks were only too eager to arrange these cookie-cutter deals for hefty fees. And investors desperate for returns enthusiastically bought in.

Suddenly, everyone from hedge fund managers like Bill Ackman to celebrities like Patrick Mahomes, the N.F.L. quarterback, and Serena Williams, the tennis legend, jumped on the SPAC bandwagon. Retail investors got involved, too, as stock trading took off during the pandemic. Even former President Donald J. Trump struck a deal with a SPAC last year to take his fledgling social media company public.

“Why did V.C.s turn to SPACs all of a sudden? Because reputable investment banks started underwriting them,” said Mike Stegemoller, a finance professor at Baylor University.

SPAC deals have been an important new source of revenue for Wall Street banks. Since the start of 2020, the top 10 banks arranging the public offerings of SPACs made just over $5.4 billion in fees, according to Dealogic. Citigroup, Credit Suisse and Goldman Sachs pocketed the biggest fees.

Companies that sell shares to the public through an I.P.O. have to undergo a rigorous process with strict rules. But SPACs face few regulations, since the companies going public have no actual operations yet. The shares are usually priced at $10 apiece.

Early investors also get warrants, a type of security that gives them the right to buy additional shares later at a predetermined price. If shares of a SPAC go up after it finds a merger partner, warrants can be financially rewarding.

The SPAC has two years to find an operating business to buy; otherwise, the money has to be returned to investors. Since investors don’t know what business a SPAC will end up buying, they have the option of redeeming their shares when they vote on the merger — meaning that the merged entity could end up with far less cash than the SPAC raised.

The SPAC boom was fueled by a long period of low interest rates, which drove investors to riskier corners of the market in search of higher returns. SPACs became especially popular with hedge funds that were looking to profit off the difference between the price of a share in a SPAC and the warrants they held.

It helped that prominent venture capitalists embraced SPACs as a quicker way to take technology start-ups public. In late 2019, Richard Branson merged Virgin Galactic, his aerospace company, with a SPAC led by Chamath Palihapitiya, the Facebook executive turned venture capitalist. The next year, DraftKings, the popular online gaming company, went public in a SPAC deal underwritten by Goldman, Credit Suisse and Deutsche Bank.

The SPAC format also provided a lifeline to companies like WeWork, which had to pull its I.P.O. in 2019 when investors balked at the office sharing company’s financials. But that was not an obstacle when WeWork merged with a SPAC last year and got $1.3 billion in badly needed capital.

“Last year was one of the best years in terms of SPACs,” said Gary Stein, a former investment bank analyst and entertainment industry consultant who has invested in such companies for nearly three decades. “This year is probably one of the more difficult ones for me to navigate.”

Two things have cooled the ardor for SPACs. Inflation is skyrocketing, prompting the Federal Reserve to raise interest rates and investors to pull their money out of SPAC deals to park elsewhere. And regulatory scrutiny of the SPAC market is increasing, which has made these deals less enticing for the players involved.

In recent months, investors have invoked more frequently their contractual right to redeem their shares in a SPAC. Historically, around 54 percent of shareholders would opt to redeem shares when a merger was announced. Now, as many as 80 percent of investors have sought their money back in some instances — a move that leaves the postmerger company with little of that promised capital.

Concerns that too many investors would seek to get cash for their shares torpedoed the merger between Kin Insurance and Omnichannel, Mr. Higgins’s SPAC. The media company BuzzFeed took in only $16 million from its merger with a SPAC, as investors reclaimed much of the $250 million it hoped to get.

Some SPAC mergers completed recently are looking grim. When MSP Recovery, a medical litigation and claims firm, closed its SPAC deal with Lionheart Acquisition Corporation II on May 24, the company’s shares fell 53 percent immediately. They are now trading around $2. Neither Lionheart nor MSP Recovery returned requests for comment.

The Securities and Exchange Commission has opened two dozen investigations involving SPACs since January 2020, according to Audit Analytics. A half-dozen involve electric vehicle companies, including Lordstown Motors, Lucid and Faraday Futures. The SPAC seeking to merge with Mr. Trump’s company is also under investigation.

Regulators have proposed rules that would make it easier for shareholders to sue companies that merged with a SPAC for making fanciful financial projections and dubious claims about production capabilities. Banks could also face increased liability for their work on such deals.

On Tuesday, Senator Elizabeth Warren of Massachusetts released a report that focused on conflicts of interest involving certain players in SPAC deals. “The process of bringing a SPAC to market inherently favors institutional investors and financial institutions — the so-called ‘SPAC mafia’ — over retail investors,” according to the report.

Some Wall Street banks are now stepping away from SPACs, concerned that they will be held liable in shareholder lawsuits for overhyped financial projections made by private companies that merge with a SPAC.

Goldman has reduced its involvement with SPACs partly because of the “changed regulatory environment,” said Maeve Duvally, a spokeswoman for the bank.

Ms. Rodrigues, the law professor, said that if Wall Street banks could be held liable for false statements made by a company that was merging with a SPAC, it would be similar to the liability they have when arranging a traditional I.P.O. Increased regulation would lead to higher costs for banks and higher fees for clients, which would dampen enthusiasm for SPACs, she said.

Of the roughly 600 SPACs still out there scrambling to find targets before the market shuts down entirely, 270 have been looking for at least a year, according to Dealogic.

Backers of those companies are desperate, which could make them less than judicious in choosing merger partners, said Nathan Anderson of Hindenburg Research, a firm that specializes in publishing critical reports about publicly traded companies including SPACs.

“The quality of SPAC deals was never high to begin with,” Mr. Hindenburg said. “And now it has the potential to get substantially worse.”

Queen Elizabeth II’s Platinum Jubilee, celebrating her 70 years on the British throne, is above all a tribute to one of history’s great acts of constancy.

Her reign has spanned virtually the entire post-World War II era, making her a witness to cultural upheavals from the Beatles to Brexit, technological advances from wireless radio to Zoom, political leaders from Winston Churchill to Boris Johnson.

From the sepia-tinted pictures of her coronation in 1953 to her emotional televised address to a nation in the grip of the pandemic in 2020, the queen has been an abiding presence in British life for as long as most Britons have been alive.

Her triumphs — history-making visits to South Africa and Ireland — have lifted the country. Her sorrows — the fraught days after the death of Diana, Princess of Wales, in a Paris car crash, or the Covid-enforced isolation of her grieving for her deceased husband, Prince Philip — have become the nation’s sorrows.

Perhaps no living person has met so many famous people, a gallery of heroes and villains ranging from Nelson Mandela to Vladimir V. Putin. But it is her countless meetings with ordinary people that have left perhaps the most lasting imprint of the longest serving British monarch in history.

The photographs below are a small representation of her reign:

The queen at Balmoral Castle in Scotland with one of her corgis in September 1952.

She was 25 years old when she ascended to the throne in 1952.

Riding in front of Prince Philip, the Duke of Edinburgh, en route to the Horse Guards Parade in London for a Trooping of the Colour ceremony in May 1956.

Attending a dinner with Winston Churchill and his wife, Clementine, at No. 10 Downing Street in London in April 1955.

The queen on a royal tour in Nigeria in 1956.

A motorcade taking Queen Elizabeth along Pennsylvania Avenue to the White House in Washington in 1957, on her first trip to the United States as the British monarch.

Elizabeth and Philip with their three children — Prince Charles, right, Princess Anne, left, and Prince Andrew — at Balmoral in September 1960.

Reviewing troops with President Heinrich Lubke of West Germany in May 1965.

Riding an elephant after a tiger hunt, part of a royal tour of Nepal in February 1961.

Queen Elizabeth and Prince Philip at the Berlin Wall during a visit to West Germany in May 1965.

With Emperor Haile Selassie of Ethiopia at the Tisisat Falls in February 1965.

Flying back from a visit to Yorkshire in a photograph taken during the filming of the documentary “Royal Family” in 1969.

Elizabeth and Philip leaving Fort Qu’Appelle, Saskatchewan, during a visit to Canada in 1978.

At the British Embassy in Kuwait in February 1979.

Touring Nizwa Fort in Oman in February 1979.

Queen Elizabeth with Prime Minister Edward Heath of Britain, left, and President Richard Nixon and the first lady, Patricia Nixon, at Chequers, the official country residence of the prime minister, in 1970.

In Mount Hagen, Papua New Guinea, in October 1982.

Riding on the grounds of Windsor Castle with President Ronald Reagan during his state visit to England in 1982.

Queen Elizabeth with West German Chancellor Helmut Kohl, left, President Ronald Reagan, and Britain’s Prime Minister Margaret Thatcher at Buckingham Palace in 1984.

At the mausoleum of the First Qin Emperor, in Xi’an, China in 1986.

With Prince William and Prince Harry at Guards Polo Club in Windsor in 1987.

Visiting maternity patient Molly Mavunda and her 4-day-old baby boy, Caswell, in Baragwanath Hospital in Johannesburg, South Africa, in 1995.

With President Nelson Mandela of South Africa at Buckingham Palace in July 1996.

Shaking hands with Innu women while visiting Sheshatshiu in central Labrador, Canada, in June 1997.

Viewing the floral tributes and other mementos to the late Diana, Princess of Wales, at Buckingham Palace in September 1997.

With the pop band the Spice Girls at the Victoria Palace Theatre in London in 1997.

Queen Elizabeth with President Vladimir V. Putin of Russia on their way to Buckingham Palace in 2003.

Visiting the Royal Albert Hall in London to mark the end of restoration work in 2004.

The Queen received a scroll from Bruce Two Dogs Bozsum at Southwark Cathedral, London, where she attended a funeral blessing for Mahomet Weyonomon, a Native American chieftain of the Mohegan tribe who died in 1736 and was laid to rest in an unmarked grave on the grounds, in 2006.

President Barack Obama and Michelle Obama, the first lady, with Queen Elizabeth and Prince Philip at Winfield House, the U.S. ambassador’s residence in London, in 2011.

Planting a tree in Dublin in 2011, as President Mary McAleese of Ireland looks on, during the first visit by a British monarch since 1911.

Sitting next to Anna Wintour, the Vogue editor in chief; Angela Kelly, a royal dressmaker; and Caroline Rush, the chief executive of the British Fashion Council, at Richard Quinn’s runway show in London in 2018.

Queen Elizabeth with Charles, the Prince of Wales, center right, and Camilla, the Duchess of Cornwall, second right, at the State Opening of Parliament in the House of Lords at Westminster in 2019.

At a D-Day commemorative event in Portsmouth, England, with President Donald Trump and the first lady, Melania Trump, in June 2019.

The Royal Family on the balcony of Buckingham Palace in June 2019 during the queen’s annual birthday parade.

Greeting President Joe Biden and the first lady, Jill Biden, at Windsor Castle in 2021.

At the funeral of Prince Philip, who died at 99, at St. George’s Chapel in Windsor Castle in 2021.

Driving her Range Rover during the Royal Windsor Horse Show at Windsor Castle in 2021.

The queen meeting with the staff of London’s Crossrail project at Paddington Station in May.

The Queen with one of her dogs, a corgi named Candy, at Windsor Castle in February.

Elon Musk’s repeated wavering on his deal to buy Twitter has roiled markets and raised fresh questions about his seriousness. His promises to preserve free speech, ban spam bots and dramatically boost revenue may have earned the blessing of the company’s founder, Jack Dorsey, but with Twitter’s stock falling well below his offer price, Mr. Musk appears to be reneging on a deal that has made even Wall Street grow skeptical.

For those of us who have followed Mr. Musk’s antics for some time, the latest twist in his bid for the social media platform is entirely in character. The way that he has managed and marketed his businesses from Tesla’s early days reveals a dysfunction behind the automaker’s veneer of technofuturism and past stock market successes. Often announcing new features without consultation with his team, he forces his employees to bridge the enormous gap between technological reality and his dreams. This disconnect fosters a negligent and sometimes cruel workplace, to disastrous effect.

In 2016, Mr. Musk promised that newly made Teslas would be able to drive themselves with nothing more than a future software update that Tesla owners could buy in advance for thousands of dollars.

That fully self-driving announcement that so delighted his fans came as a far more jarring revelation to the project’s engineers, who found out about their staggering new mission when Mr. Musk tweeted about it. Tesla buyers never got the promised software update. The cars still cannot drive themselves without humans. But every year since then, he has repeated different versions of this claim. His ability to repeatedly sell such science fiction fantasies to a credulous public is the foundation for a vast empire and fortune.

Tesla’s manufacturing engineers were aghast when, also in 2016, Mr. Musk publicly committed to developing a fully automated factory that required no human workers. Tesla built two assembly lines that attempted to automate tasks requiring levels of dexterity and flexibility that modern robotics is still far from attaining. He ultimately gave up and cobbled together a manual-labor-intensive production line in an open-air tent.

Mr. Musk took this as a new opportunity to build his legend, and he reported that he had slept in Tesla’s factories during this period, which he called “production hell.” What he left out of his self-aggrandizing was the reality for his employees. His presence brought no real manufacturing expertise to bear, just the overbearing pressure of a boss whose public shaming was punctuated by declarations like “I can be on my own private island with naked supermodels, drinking mai tais — but I’m not.”

In my reporting on Tesla, interviewing employees at times felt more as if I had been a therapist than a journalist, as they sought to untangle the pride and satisfaction they felt about their work from the trauma of working for Mr. Musk. Surviving 10 years of the grind at Tesla is a rare achievement, and it is common for talent to be squeezed dry or pushed out before the end of the company’s four-year stock vesting period.

This grim environment is all the more pronounced for women and racial minorities. Lawsuits by workers and California’s Department of Fair Employment and Housing allege that Black workers were tasked with menial physical labor in parts of the factory nicknamed “the plantation,” where they were subjected to racist slurs and graffiti. Female workers have sued, alleging a pervasive culture of sexual harassment and groping by supervisors. Mr. Musk was indifferent, emailing workers who experienced abuse that “it is important to be thick-skinned.”

Mr. Musk’s interest lies in supervising entrepreneurial projects that result in flashy new components. In more prosaic areas of the business like manufacturing, service and sales, he tends to get involved only in order to put out the fires that regularly threaten the company’s immediate future (though not the literal fires that have repeatedly ravaged its Fremont, Calif., factory over the years).

This is the fundamental weakness of every organization run as a cult of personality: The dear leader can’t be everywhere or make every decision but often fails to provide the clear code of values that allows managers to independently shape their decisions around common goals. When the success of the company is tied to one man’s whims, you get bizarre phenomena like managers deciding whether or not to take issues to Mr. Musk based on the shade of blond of his wife’s hair that day (with platinum shades being correlated with better moods).

When the boss happens to run tunneling, rocket and brain-implant companies in addition to a high-profile car company, even the most brilliant minds will occasionally be too disconnected from the realities of the decisions that they must make. After the collapses of Theranos and WeWork — companies with similarly confident founders who insisted that they would achieve their soaring ambitions if given more time and money — Mr. Musk’s reliance on hype is especially jarring.

Indeed, the main difference between Mr. Musk and Silicon Valley’s fallen heroes is that he has been able to deliver on some promises: Tesla does make cars, and SpaceX does land rockets. But as a number of old promises like fully self-driving cars appear to be more aspirational and less plausible, the distinction between him and those fallen heroes is starting to lose its meaning. His long list of unfulfilled commitments — a fully solar-powered electric vehicle charging network, a fully automated manufacturing system, an autonomous minibus and even a rocket-powered flying car — wildly exceed his achievements.

By moving to buy Twitter, Mr. Musk has not only added another distraction to his long list but has also already shown the same drive to announce sweeping decisions in public. While he had some success in realizing user features at Tesla, his contradictory goals of increasing algorithmic transparency and eliminating spam bots on Twitter are the most obvious sign that he intends to impose his will on the service without drawing on the expertise of workers who have been wrestling with Twitter’s thorniest challenges.

Ultimately Mr. Musk’s goals for Twitter, as they are for Tesla, are not about making the right decisions for his companies or the people who make them possible. They are about playing to the crowd and burnishing the legend that keeps fresh bodies and minds moving through the businesses that chew them up and spit them out. Now if Twitter falls into his control, Mr. Musk will have seized the means of making the product he has always cared about most: his own myth making.

Edward Niedermeyer (@Tweetermeyer) is the author of “Ludicrous: The Unvarnished Story of Tesla Motors” and a co-host of “The Autonocast,” a podcast about driving automation technology and the future of mobility.

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During his first six months as mayor, Eric Adams has developed a reputation for being a fixture of New York City’s nightlife scene.

So it should perhaps not come as a surprise that Mr. Adams has proposed changing the city’s zoning regulations to allow New Yorkers to dance more easily in bars and restaurants.

Although the city had repealed its Cabaret Law, a 1926 regulation that made it illegal to host dancing, singing or musical entertainment without a license, zoning law restrictions left many establishments unable to permit dancing.

“Think about the owner of a tapas bar that has live music on weekends and wants to set aside a small space for dancing, but finds that under city rules, it’s not allowed,” Mr. Adams said on Wednesday during a speech before the Association for a Better New York. “We’re going to change that no to a yes, and let the people dance.”

Supporting the city’s nightlife is not just about fun, the mayor has said. It is also part of an effort to help small business owners still trying to recover from more than two years of the pandemic’s devastating effects on the economy.

But too many bars and restaurants are hampered by antiquated zoning regulations that prohibit dancing, among other things, Mr. Adams said on Wednesday, adding that he intended to change out-of-date zoning rules that interfered with the city’s recovery.

“Far too many agencies don’t understand part of their mandate is to allow the city to grow and flourish,” Mr. Adams said. “Don’t start with no. Start with how do we get to yes. How do we build our city?”

The proposed changes to the city’s zoning rules would, for example, allow a small retailer looking to expand its business selling to other businesses do so without relocating to an area zoned for manufacturing; they would allow homeowners to convert the second floor of their homes to rental units without having to add a parking space; and the changes would make it easier to convert unused office space into housing.

Other zoning changes would make it easier to install solar panels and create charging stations for electric vehicles. Mr. Adams said the city also wants to use smart zoning to increase opportunities around four new Metro-North stations expected to open in the Bronx in 2027.

City planning officials will begin a public engagement process to craft the language of the zoning text amendments. There will be an environmental review for the proposed changes and the City Council will have to approve the changes.

New York suffered as a result of the pandemic but is starting to see some job growth, said James Parrott, an economist with the Center for New York City Affairs at the New School. The city added 39,400 jobs in April, including 7,200 in the full service restaurant industry.

The changes to the zoning regulations that make it legal for bars and restaurants to allow dancing are a continuation of the repeal of the Cabaret Law from 1926 that made it illegal to host dancing, singing or musical entertainment without a license. It is widely believed that the law was used to target racially mixed jazz clubs in Harlem.

The rule was liberally applied across the city’s venues, and music was not allowed at bars without a cabaret license until 1936. The city required cabaret employees and performers to carry “cabaret cards” and also be fingerprinted. A prior police record could be used to deny applicants cabaret cards, and famous musicians such as Ray Charles and Billie Holiday were not eligible.

Mayor Rudolph W. Giuliani used the cabaret law to enforce his quality of life initiatives, but Mayor Bill de Blasio repealed the law in 2017. Even after the law was repealed, the city’s zoning rules still prevented dancing in some restaurants or bars.

The proposed changes will remove dancing from consideration under the zoning laws and will instead rely on indicators such as whether venues have cover charges or show times and thus might need a license, city officials said.

Ariel Palitz, executive director of the Office of Nightlife at the Mayor’s Office of Media and Entertainment, said in an email that Mr. Adams was essentially carrying out “unfinished business” left behind from the repeal of the Cabaret Law.

Large establishments that want to offer dancing will still come under review as they apply for a liquor license, and be subject to fire and noise rules and community review, said Keith Powers, the City Council’s majority leader.

Business owners expressed relief at the coming changes.

“All of these tiny, weird things affect how you operate,” said Diana Mora, who helped found NYC Nightlife United, and runs Friends and Lovers in Crown Heights, Brooklyn. A fuller repeal of the Cabaret Law helps remove the fear that even though businesses are trying to follow the rules, “someone’s going to come in, something’s going to happen. You’re going to be shut down.”

John Barclay, owner of Paragon, was involved in the Dance Liberation Network that pushed for repealing the Cabaret Law in 2017. He said the law was being “enforced against very predictable groups,” such as venues frequented by Black and Latino people.

“If a law or a regulation is founded with clear, bigoted intent or if the results of enforcement are clearly racist or bigoted in any way, it needs to be repealed point blank,” he said.

Sheryl Sandberg, the chief operating officer of Meta and the longtime second in command to its founder, Mark Zuckerberg, said on Wednesday that she was stepping down from the company after 14 years.

Ms. Sandberg said she was leaving Meta this fall and that she planned to continue serving on the company’s board of directors. Meta owns Facebook, Instagram, WhatsApp and other apps.

“When I took this job in 2008, I hoped I would be in this role for five years. Fourteen years later, it is time for me to write the next chapter of my life,” Ms. Sandberg wrote in a Facebook post.

She added that she was “not entirely sure what the future will bring” but that she would focus on her foundation and philanthropy. Ms. Sandberg also said she was getting married this summer.

Ms. Sandberg served as the key lieutenant to Mr. Zuckerberg at Facebook, which she joined after building the advertising business at Google. Ms. Sandberg was often cited as being the adult in the room during Facebook’s early days, tasked with turning a fast-growing start-up into a profitable enterprise.

This is a developing story. Check back for updates.

WASHINGTON — The Russian military, beaten down and demoralized after three months of war, is making the same mistakes in its campaign to capture a swath of eastern Ukraine that forced it to abandon its push to take the entire country, senior American officials say.

While Russian troops are capturing territory, a Pentagon official said that their “plodding and incremental” pace was wearing them down, and that the military’s overall fighting strength had been diminished by about 20 percent. And since the war started, Russia has lost 1,000 tanks, a senior Pentagon official said last week.

President Vladimir V. Putin of Russia appointed a new commander, Gen. Aleksandr V. Dvornikov, in April in what was widely viewed as an acknowledgment that the initial Russian war plan was failing.

Soon after his arrival, General Dvornikov tried to get disjointed air and land units to coordinate their attacks, American officials said. But he has not been seen in the past two weeks, leading some officials to speculate as to whether he remains in charge of the war effort.

Russian pilots also continue to demonstrate the same risk-averse behavior they did in the early weeks of the war: darting across the border to launch strikes and then quickly returning to Russian territory, instead of staying in Ukrainian air space to deny access to their foes. The result is that Russia still has not established any kind of air superiority, officials said.

The Russian military has made some progress in the east, where concentrated firepower and shortened supply lines have helped its forces fight intense battles in recent days. After three bloody months, Russia finally took Mariupol in mid-May, potentially creating a land bridge from the Russian-controlled Crimean Peninsula to the south.

As Russia struggles to move forward, Ukraine has also suffered setbacks. President Volodymyr Zelensky of Ukraine recently said that as many as 100 Ukrainian servicemen might be dying every day in the fighting. And on Tuesday, Russian troops advanced toward the center of Sievierodonetsk, a city that has become a central focus for the military since it shifted its attention to the east.

But some of the areas that Russian forces managed to seize have been quickly contested again, and sometimes retaken, by Ukrainian troops.

Consider Kharkiv. Russia spent six weeks bombarding the eastern city, once home to 1.5 million people, as troops encircled it.

But by May 13, control of the city had flipped again. “The Russians took Kharkiv for a short period of time; the Ukrainians counterattacked and took Kharkiv back,” Defense Secretary Lloyd J. Austin III said at a news conference at the Pentagon last week. “We’ve seen them really proceed at a very slow and unsuccessful pace on the battlefield.”

Ukraine is now pushing Russian troops north and east from Kharkiv, “in some cases all the way back to Russia,” said retired Gen. Philip Breedlove, the former supreme allied commander for Europe. “So now Ukrainians are threatening to cut off Russian lines of supply and pushing their forces to the rear.”

Cutting off Russian supply lines east of Kharkiv would put Russian troops in the same situation they were in after their advance on Kyiv, the capital of Ukraine, at the beginning of the war, officials said. Ukrainian units carrying shoulder-fired Javelin antitank missiles picked off Russian soldiers as miles-long Russian convoys near Kyiv stopped moving forward. The invasion stalled, and thousands of Russian troops were killed or injured. Russia then refocused its mission on the east.

In the early weeks of the war, Russia ran its military campaign out of Moscow, with no central war commander on the ground to call the shots, American and other Western officials said. In early April, after Russia’s logistics and morale problems had become clear, Mr. Putin put General Dvornikov in charge of a streamlined war effort.

General Dvornikov arrived with a daunting résumé. He started his career as a platoon commander in 1982 and later fought in Russia’s brutal second war in Chechnya. Moscow also sent him to Syria, where the forces under his command were accused of targeting civilians.

In Ukraine, he established a more streamlined process. Russian pilots began coordinating with troops on the ground toward a similar objective in the eastern region of Donbas, and Russian units were talking to one another about shared goals.

But the invasion is not “proceeding particularly differently in the east than in the west because they haven’t been able to change the character of the Russian army,” said Frederick W. Kagan, a senior fellow and director of the Critical Threats Project at the American Enterprise Institute. “There are some deep flaws in the Russian army that they could not have repaired in the last few weeks even if they had tried. The flaws are deep and fundamental.”

At the top of that list is the Russian army’s lack of a noncommissioned officers corps empowered to think for itself, Pentagon officials said. American troops have sergeants and platoon leaders and corporals who are given tasks and guidelines and left to accomplish those tasks as they see fit.

But Russia’s military follows a Soviet-style doctrinal method in which troops at the bottom are not empowered to point out flaws in strategy that should be obvious or to make adjustments.

The Ukrainians, after seven years of training alongside troops from the United States and other NATO countries, follow the more Western method and have proved particularly agile at adapting to circumstances, American military officials said.

A two-week fighting pause after the Russian military gave up the fight for Kyiv was not long enough to turn the campaign around, even with a more limited goal, General Breedlove said. General Dvornikov’s “new tactics, resetting the command and control so there was a focused decision maker — all that was right or proper,” he said.

But, General Breedlove added: “Even our army would be hard-pressed to refit, refurbish and reorganize in two weeks after having received such a sound whipping.” When General Dvornikov took control, “the force was thrust back into the battle too quickly. That decision had to have come from Moscow.”

After renewing an assault on the Donbas, Russia has pounded cities and villages with a barrage of artillery. But troops have not followed that up with any kind of sustained armored invasion, which is necessary if they will hold the territory they are flattening, military officials say. That means that Russia may find itself struggling to hold on to gains — as it did in Kharkiv.

Evelyn Farkas, a former senior Pentagon official for Ukraine and Russia in the Obama administration, said Mr. Putin was still too involved in the fight.

“We keep hearing accounts of Putin getting more involved,” said Ms. Farkas, who is now executive director of the McCain Institute. “We know that if you have presidents meddling in targeting and operational military decisions, it’s a recipe for disaster.”

Before invading Ukraine on Feb. 24, Russian forces already controlled about 30 percent of the eastern Ukrainian region known as Donbas. Russia had taken the territory — with help from local separatist forces — as part of a sporadic, often low-grade war with Ukraine that began in 2014.

Today, Russia controls closer to 75 percent of Donbas. Some of the most recent Russian gains have come around Sievierodonetsk.

Together, those two statistics — 30 percent and 75 percent — offer a useful summary of the war.

Yes, the war has gone much worse for Russia than almost anybody expected: Rather than overrunning Kyiv, Ukraine’s capital, in mere days, the Russian military had to backtrack and narrow its goals to Donbas, a long-disputed border region. But Russia is nonetheless making progress there. It may yet accomplish the more limited goal of dominating Donbas. And Vladimir Putin is betting that he will prove more patient than Ukraine’s Western allies.

Today’s Times has several notable pieces of Ukraine coverage. Helene Cooper looks at the military mistakes that Russia is repeating, and Carlotta Gall profiles the Ukrainians choosing to stay in their homes in Donbas. Three photographers — Lynsey Addario, Finbarr O’Reilly and Ivor Prickett — have published images and stories from the front lines.

In the Opinion section, President Biden has published an essay explaining that his administration will continue to send weapons to Ukraine but not troops. In the essay, he announces that the U.S. will send longer-range missiles to Ukraine than it previously has.

Alongside those pieces, we’re using today’s newsletter to give you an overview of the war.

A Russian pincer

The big question over the next several weeks — according to our colleague Julian Barnes, who covers U.S. intelligence agencies — will be whether Russia can encircle Ukraine’s forces in Donbas. If Russia can, the Ukrainian troops could be cut off from the rest of the country and suffer heavy losses. Russia might then be in position to take control of nearly all of Donbas.

“Intelligence officials have repeatedly said, both publicly and privately, that this next phase is going to be very important in setting the tenor for the war in the months to come,” Julian said. “It will determine whether we stay in something approximating a stalemate or if one side gets the upper hand.”

In the war’s early weeks, Russia tried to move quickly and capture large sections of territory. Its military proved incapable of doing so, rebuffed by Ukrainian troops, with help from weapons provided by the U.S., E.U. and other allies. In the war’s current phase, Russia has emphasized a strategy from other recent wars, in Syria and Chechnya: using missiles and other heavy artillery to bombard cities and towns and eventually take them over.

As Anton Troianovski, The Times’s Moscow bureau chief, says: “The war has clearly gone on much longer than anyone anticipated, including the Russians. And the Russians after those initial failures have adapted and have gone back to the traditional method of fighting wars.”

The bombardment appears to be causing substantial Ukrainian casualties. On a typical recent day, between 50 and 100 Ukrainian troops were killed, President Volodymyr Zelensky recently estimated. Russia has also managed to capture some economically significant areas, including ports and wheat fields.

Putin has adopted a strategy that Russia has used for much of its history, combining its vast resources with a high tolerance of casualties to make slow wartime gains. In this war, Putin believes that Ukraine’s Western allies become weary of the fight long before he feels much pressure to do so. “He’s betting on the West to get tired and to get distracted,” Anton said.

Still, Putin faces many of the same problems that undermined Russia’s initial invasion, as Helene Cooper’s story explains. Its military has proved to be an inefficient, top-down organization in which field commanders often must wait for high-level orders. Much of Russia’s equipment is out of date, and many of its troops are not well trained. They also did not expect to be part of a full-scale war, and the deaths of thousands of their fellow soldiers have further weakened morale.

“The Russians are attempting to subdue a massive country with a well-organized military that is fighting on its home turf,” Helene said. “That is a very tall order for an army where you have soldiers on the ground with no clue why they are even in Ukraine.”

Barriers to peace

Ultimately, many analysts believe that Russia’s military problems will make it very difficult for Putin to control large parts of Ukraine for months or years. Yet Donbas is where he is most likely to find some success.

“The overall military balance in this war still trends in Ukraine’s favor, given manpower availability and access to extensive Western military support,” Michael Kofman, the director of Russia studies at CNA, a research group, recently wrote. “That will show itself more over time. But the local balance in the Donbas during this phase is a different story.”

The most likely medium-term scenario is that Russia will control a large amount of Donbas and that Putin will patiently and brutally try to expand Russia’s holdings. He — as well as Ukraine and its allies — would then need to decide whether any truce is possible.

“I will not pressure the Ukrainian government — in private or public — to make any territorial concessions,” Biden wrote in his Times essay.

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