For the past couple of weeks, some Americans have reported a curious phenomenon: They have caught the coronavirus despite being vaccinated.

Vaccines are still doing their job by protecting against serious illness and hospitalization, but the frequency of so-called breakthrough infections has surprised experts.

How do such cases happen, and what risks do they pose?

Guest: Apoorva Mandavilli, a science and global health reporter for The New York Times.

Breakthrough Infections, Explained

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Debates over homeless encampments in the United States have intensified as their number has surged. To tackle the problem, some cities have enforced bans on public camping.

As the Supreme Court prepares to hear arguments about whether such actions are legal, Abbie VanSickle, who covers the court for The Times, discusses the case and its far-reaching implications.

Guest: Abbie VanSickle, a Supreme Court correspondent for The New York Times.

The Supreme Court Takes Up Homelessness

Political and legal history are being made in a Lower Manhattan courtroom as Donald J. Trump becomes the first former U.S. president to undergo a criminal trial.

Jonah Bromwich, who covers criminal justice in New York, explains what happened during the opening days of the trial, which is tied to Mr. Trump’s role in a hush-money payment to a porn star.

Guest: Jonah E. Bromwich, who covers criminal justice in New York for The New York Times.

The Opening Days of Trump’s First Criminal Trial

The Environmental Protection Agency has begun for the first time to regulate a class of synthetic chemicals known as “forever chemicals” in America’s drinking water.

Kim Tingley, a contributing writer for The New York Times Magazine, explains how these chemicals, which have been linked to liver disease and other serious health problems, came to be in the water supply — and in many more places.

Guest: Kim Tingley, a contributing writer for The New York Times Magazine.

Are ‘Forever Chemicals’ a Forever Problem?

A Times investigation shows how the country’s biggest technology companies, as they raced to build powerful new artificial intelligence systems, bent and broke the rules from the start.

Cade Metz, a technology reporter for The Times, explains what he uncovered.

Guest: Cade Metz, a technology reporter for The New York Times.

A.I.’s Original Sin

Overnight on Saturday, Iran launched its first direct attack on Israeli soil, shooting hundreds of missiles and drones at multiple targets.

Eric Schmitt, a national security correspondent for The Times, explains what happened and considers whether a broader war is brewing in the Middle East.

Guest: Eric Schmitt, a national security correspondent for The New York Times.

Breakthrough Infections, Explained

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