A decision that Mr. Trump was ineligible to hold office would have been a political earthquake altering the course of American history.

The court’s decision will determine whether and when Mr. Trump will face trial for his attempts to overturn his 2020 loss at the polls.

In a series of decisions, the court has narrowed the reach of federal criminal laws aimed at public corruption and white-collar crime.

The case has the potential to knock out half of the federal charges against former President Donald J. Trump for plotting to subvert the 2020 election and could complicate hundreds of Jan. 6 prosecutions.

The case will determine whether access to the drug, which is used in the majority of abortions in the United States, will be sharply curtailed.

The Supreme Court will decide whether a federal law that requires emergency rooms to provide stabilizing care to all patients overrides a state law, in Idaho, that imposes a near-total ban on abortion.

It is the first time the Supreme Court is considering a state law criminalizing abortion since it overturned Roe v. Wade. The decision may affect more than a dozen states that have passed near-total bans on abortion.

Lower courts have struck down federal laws prohibiting people who have been convicted of felonies or who use drugs from owning guns.

The court may start to clear up the confusion it created in the Bruen decision, in the first major test of its expansion of gun rights. The standard it announced has left lower courts in turmoil as they struggle to hunt down references to obscure or since-forgotten regulations.

The Supreme Court will decide whether ordinances in Oregon aimed at preventing homeless people from sleeping and camping outside violate the Eighth Amendment’s prohibition on cruel and unusual punishment.

The case could have major ramifications on how far cities across the country can go to clear homeless people from streets and other public spaces.

The cases arrive garbed in politics, as they concern laws aimed at protecting conservative speech. But the larger question the cases present transcends ideology. It is whether tech platforms have free speech rights to make editorial judgments.

The Supreme Court is also considering a case that raises similar issues, National Rifle Association v. Vullo, about whether a state official in New York violated the First Amendment by encouraging companies to stop doing business with the National Rifle Association.

The case is a major test of the role of the First Amendment in the internet era, requiring the court to consider when government efforts to limit the spread of misinformation amount to censorship of constitutionally protected speech.

The Supreme Court will decide whether a New York State official violated the First Amendment by trying to persuade companies not to do business with the National Rifle Association after the school shooting in Parkland, Fla.

The case is one of two that will determine when government advocacy edges into violating free speech rights. The other, Murthy v. Missouri, concerns the Biden administration’s dealings with social media companies.

The case centers on when persuasion by government officials crosses into coercion.

The case is the first time the Supreme Court will address whether a bankruptcy plan can be structured to give civil legal immunity to a third party, without the consent of all potential claimholders. The legal maneuver under scrutiny has become increasingly popular in bankruptcy settlements.

Approving the deal would funnel money toward states and others who have waited for years for some kind of settlement. Yet the Sacklers would be largely absolved from future opioid-related claims. More broadly, the case may have implications for similar agreements insulating a third party from liability.

Yes. A series of Supreme Court decisions say that making race the predominant factor in drawing voting districts violates the Constitution.

The case concerns a constitutional puzzle: how to distinguish the roles of race and partisanship in drawing voting maps when Black voters overwhelmingly favor Democrats. The difference matters because the Supreme Court has said that only racial gerrymandering may be challenged in federal court under the Constitution.

Yes. Chevron is one of the most cited cases in American law.

Overturning the decision could threaten regulations on the environment, health care, consumer safety, nuclear energy, government benefit programs and guns. It would also shift power from agencies to Congress and to judges.

There is no precedent squarely on point.

A ruling against the bureau, created as part of the 2010 Dodd-Frank Act after the financial crisis, could cast doubt on every regulation and enforcement action it took in the dozen years of its existence. That includes agency rules — and punishments against companies that flout them — involving mortgages, credit cards, consumer loans and banking.

A ruling against the S.E.C. would not only require it to file cases in federal court but could also imperil administrative tribunals at many other agencies, including the Federal Trade Commission, the Internal Revenue Service, the Environmental Protection Agency, the Social Security Administration and the National Labor Relations Board.

Prevailing winds carry emissions of nitrogen oxide toward Eastern states with fewer industrial sites. The pollutant causes smog and is linked to asthma, lung disease and premature death.

The case involves how to interpret a federal law that banned machine guns, the National Firearms Act of 1934. The definition was broadened by the Gun Control Act of 1968 to include parts that can be used to convert a weapon into a machine gun. At issue is whether bump stocks fall within those definitions. Federal appeals courts have split on the issue.

A decision could do away with one of the few efforts at gun control that gained political traction after the Las Vegas massacre in 2017. More broadly, a ruling could help clarify the scope of the power of federal agencies.