Interest in visiting the islands is running high, but the price of paradise can be multiple Covid tests, expensive stints in quarantine, long waits in line and more.

Want to Go to Hawaii? Be Prepared.

Members of the European Union are welcoming Americans. But there are still rules and restrictions to abide by. Here’s how to navigate them and what to expect.

A Country-by-Country Guide to Reopened Europe

A new AMC satire mocks the family sitcom cliché of schlubby husbands paired with beautiful wives. Here are a few of the more egregious examples.

Kevins Can Score Improbably Attractive TV Wives

The mainstream narrative is that a pop star ripped up a photo of the pope on “Saturday Night Live” and derailed her life. What if the opposite were true?

Sinead O’Connor Remembers Things Differently

Little Island, developed by Barry Diller, with an amphitheater and dramatic views, opens on Hudson River Park. Opponents battled it for years.

A New $260 Million Park Floats on the Hudson. It’s a Charmer.

The embattled lingerie giant is attempting the most extreme brand turnaround in recent memory: an effort to redefine not just itself but also the very idea of what “sexy” is.

Victoria’s Secret Swaps Angels for ‘What Women Want.’ Will They Buy It?

The headaches began with problems with a weather data supplier on Monday, then technical troubles on Tuesday, and the issues spilled over into Wednesday.

Southwest Airlines Delays and Cancels Flights for a Third Day

Ms. Scott made a new round of grants, to 286 organizations. Her net worth, which Forbes estimates at $60 billion, keeps rising, thanks to Amazon stock.

MacKenzie Scott Gives Away Another $2.74 Billion Even as Her Wealth Grows

The president’s plans to invest in infrastructure, education, health care and more would push federal spending to its highest sustained levels since World War II.

Biden to Propose $6 Trillion Budget to Make U.S. More Competitive

A new $3.2 billion program will support the development of antiviral pills, which could start arriving by the end of this year.

A Pill to Treat Covid-19? The U.S. Is Betting on It.

An analysis of health insurance records of almost two million coronavirus patients found new issues in nearly a quarter — including those whose Covid infection was mild or asymptomatic.

Many Post-Covid Patients Are Experiencing New Medical Problems, Study Finds

More than half of the cases were reported in people ages 12 to 24. Not all are likely to be verified or related to vaccines, and experts believe the benefits of immunization far outweigh the risk of these complications.

The C.D.C. is investigating nearly 800 cases of rare heart problems following immunization.

The drug, Aduhelm, a monthly infusion priced at $56,000 per year, was approved this week despite weak evidence that it helps patients.

Three F.D.A. Advisers Resign Over Agency’s Approval of Alzheimer’s Drug

Important immune cells survive in the bone marrow of people who were infected with the virus or were inoculated against it, new research suggests.

Immunity to the Coronavirus May Persist for Years, Scientists Find

The agency is reviewing several dozen reports that teenagers and young adults may have developed myocarditis after vaccination, officials said. But the agency has not determined whether the vaccine caused the condition.

C.D.C. Is Investigating a Heart Problem in a Few Young Vaccine Recipients

I have three kids under 10 who don’t expect — or even want — to play with me. It took some practice, but over time, we’ve all learned we’re better off doing our own thing.

Don’t Play With Your Kids. Seriously.

Floating corpses in India's holiest river are Exhibit A for the Modi administration’s failures and deceptions.

The Ganges Is Returning the Dead. It Does Not Lie.

During the pandemic, Americans have been asking existential questions about their lives; now they are changing them.

The American Renaissance Has Begun

Emancipation from slavery has been celebrated on different days in different places.

What Walmart Doesn’t Get About Juneteenth

Why do we leave millions of people in poverty? The answer should make us uncomfortable.

What the Rich Don’t Want to Admit About the Poor

They, too, work, and they can help fill shortages everywhere.

It’s Time to Trust China’s and Russia’s Vaccines

Schools and the entertainment industry, which help shape what is history and what is forgotten, must portray the burden of racism in our nation. 

Tom Hanks: You Should Learn the Truth About the Tulsa Race Massacre

At 17, biologist Juliane Diller was the sole survivor of a plane crash in the Amazon. Fifty years later she still runs Panguana, a research station founded by her parents in Peru.

She Fell Nearly 2 Miles, and Walked Away

Researchers are starting to investigate the species that drive alpine algal blooms to better understand their causes and effects.

Glacier Blood? Watermelon Snow? Whatever It’s Called, Snow Shouldn’t Be So Red.

People out west in the United States and in Australia and East Asia will have a good view of an event some call a “super blood moon.”

When to Watch a Lunar Eclipse and Supermoon in Late Night Skies

The midfielder was walking near the sideline when he fell over. Medical teams offered urgent treatment on the field.

Denmark’s Christian Eriksen collapsed on the field. He is responsive and awake.

The four-time Grand Slam tournament winner wrote on Instagram that she had suffered from bouts of depression since 2018 and that she would “take some time” away from the tennis court.

Naomi Osaka Quits the French Open After News Conference Dispute

The Olympic gold medalist’s new vault is so dangerous that gymnastics, for now, limits the scoring rewards for trying it. Biles says that’s unfair.

Simone Biles Dials Up the Difficulty, ‘Because I Can’

The decision was aimed at the nation’s second Catholic president and exposed bitter divisions in American Catholicism.

Targeting Biden, Catholic Bishops Advance Controversial Communion Plan

A man who finished last in his fantasy football league had to spend 24 hours at a Waffle House restaurant. For every waffle he ate, his sentence was reduced by an hour.

15 Hours and 9 Waffles Later, a Fantasy Football Punishment Is Complete

Production problems and a brief pause on its use kept the one-dose vaccine from becoming the game changer that health officials across the country believed it would be.

High Hopes for Johnson & Johnson’s Covid Vaccine Have Fizzled in the U.S.

Some objected to the phrase “Independence Day” in the formal name of the holiday celebrating the end of slavery. Others said federal workers did not need another paid day off.

These 14 House Republicans Voted Against a Juneteenth Federal Holiday

On June 19, 1865, enslaved African-Americans in Galveston, Texas, were told they were free. A century and a half later, people in cities and towns across the U.S. continue to celebrate the occasion.

So You Want to Learn About Juneteenth?

The officers voted to leave the unit, known as the Rapid Response Team, hours after one of its members was charged with assaulting a woman at an Oregon protest in August.

50 Police Officers Step Down From a Crowd Control Unit in Portland

A junior high cheerleading team took nearly identical photos with and without Morgyn Arnold. The school called the publication of the photo without her a mistake that is under investigation.

Two Team Photos, One Difference: The Cheerleader With Down Syndrome

Democrats know that their election overhaul has no chance as long as the filibuster exists, but they are eager to show that all that stands in its way are Republicans.

Joe Manchin and the Magic 50th Vote for Democrats’ Voting Rights Bill

The birthrate is falling for American women in their 20s, especially in places where the local economy is booming.

Why American Women Everywhere Are Delaying Motherhood

After two white families claimed a grade calculation error, a Mississippi school added their children as co-valedictorian and co-salutatorian, reviving questions about race and equity.

Two Black Students Won School Honors. Then Came the Calls for a Recount.

The company notified Donald F. McGahn II last month that it had been subpoenaed for his account information three years ago.

Apple Is Said to Have Turned Over Data on Trump’s White House Counsel in 2018

The Justice Department seized records from Apple for metadata of House Intelligence Committee members, their aides and family members.

Hunting Leaks, Trump Officials Focused on Democrats in Congress

The Cascade County Sheriff’s Office said it appeared to be the oldest homicide case in the United States to be solved with genetic genealogy.

Two Montana Sweethearts Were Fatally Shot in 1956. The Case Was Just Solved.

A suspect and a sheriff’s deputy were wounded as they exchanged gunfire in a suburb of Atlanta, the authorities said.

Man Kills Georgia Grocery Worker in Mask Argument, Police Say

A recent graduate in Alpine, Texas, who could not find an affordable lawyer represented herself in court, arguing that school officials made errors in tabulating grade-point averages.

Her High School Said She Ranked Third in Her Class. So She Went to Court.

Photos of at least 80 female students at a Florida school had been digitally edited. The school superintendent said there was no “intent to embarrass or shame” them for the clothes they wore.

Yearbook Photos of Girls Were Altered to Hide Their Chests

The Justice Department also said it was changing its policy to bar seizing reporters’ phone and email records in hunts for their sources.

White House Disavows Knowledge of Gag Order on Times Leaders in Leak Inquiry

Emails show the increasingly urgent efforts by President Trump and his allies during his last days in office to find some way to undermine, or even nullify, the election results.

Meadows Pressed Justice Dept. to Investigate Election Fraud Claims

Drinking coffee has been linked to a reduced risk of all kinds of ailments, including Parkinson’s disease, melanoma, prostate cancer, even suicide.

The Health Benefits of Coffee

The bloc recommended that its 27 member nations lift a ban on nonessential travel from the United States, but each country will decide for itself.

The European Union Recommends Opening to Americans to Rescue the Summer

Four-fifths of symptomatic cases develop fevers, more than in earlier outbreaks. The findings match trends in other countries where the Delta variant is spreading.

In China’s latest outbreak, doctors say the infected get sicker, faster.

The virologist, Shi Zhengli, said in a rare interview that speculation about her lab in Wuhan was baseless. But China’s habitual secrecy makes her claims hard to validate.

A Top Virologist in China, at Center of a Pandemic Storm, Speaks Out

Fewer babies’ cries. More abandoned homes. Toward the middle of this century, as deaths start to exceed births, changes will come that are hard to fathom.