The court was to hear a showdown over President Trump's travel ban, but the courtroom argument scheduled for Oct. 10 was canceled after the White House issued new visa restrictions on Sept. 24. On Thursday, lawyers for both sides will tell the court what they think should be done with the challenges to the president's authority to issue the executive order.
Here are some of the issues up before the highest court in the land this term:
The baker, Jack Phillips of Masterpiece Cakeshop, said his cakes are works of art and the state law compels him to express a view he opposes. "I don't want to be forced to create art, sculpting, painting, any of the things that I do for an event that goes against my faith."
New Jersey's governor, Chris Christie, is urging the court to rule that the federal government cannot prevent his state from allowing sports betting at casinos and racetracks, where it would generate millions in tax revenue. Professional sports leagues and the NCAA say in response that a federal law bans sports betting in most states.
At a time when 95 percent of Americans own a cellphone, the court will decide whether the police need a search warrant to plot the movements of a phone's user, by analyzing data the phone companies collect as roving calls are handed off to successive cell towers.
Lower courts have generally said police don't need a warrant, relying on a Supreme Court ruling four decades ago. It said telephone customers don't expect that the numbers they dial will remain private, since the phone company needs the information for billing. The court will decide whether that reasoning should apply in the digital age, when phones are no longer hard-wired into the wall.
Nathan Wessler of the ACLU said police should be required to get a warrant from a judge before accessing the data.
"Knowing where a person's phone goes can tell you a great deal of private information about them, from where someone slept at night, whether at home, or in someone else's house three miles away, to whether someone goes to a doctor, a psychiatrist."
In a case that could deal a crippling blow to unions representing millions of the nation's public employees, the justices will decide whether state government workers who choose not to join a union must still pay a share of union dues to cover the cost of negotiating contracts. At stake is the future power and financial health of public sector unions in the 22 states where they have a duty to bargain for both members and nonmembers alike.
Anti-union groups argue that requiring nonunion members to pay a portion of union dues forces them to endorse views they don't agree with, violating their First Amendment rights. But the unions say negotiating contracts, which provide benefits to nonunion members as well, is expensive. They argue that the fees prevent "free riders."
And in a case that could change the future of American politics, the justices will consider whether states can become so blatantly partisan in drawing the boundary lines for voting districts that they violate the Constitution.
Wisconsin is split nearly equally between Republican and Democratic voters, but after gaining control of the legislature and the governor's office, Republicans redrew State Assembly district lines in 2011, eventually giving them 64 out of 99 seats. Lower courts said the result was so excessively partisan that it denied Democrats a fair shot at electing candidates of their choosing.
"We've reached a point here, and Wisconsin is an extreme example, where a political party ends up deciding in advance who's going to win or lose the election," said Trevor Potter of the Campaign Legal Center, which is challenging the new map.
Courts have long held that oddly shaped districts are unconstitutional if they put racial minorities at a disadvantage. But it has never set out a legal standard for blowing the whistle on excess political partisanship.
Rick Hasen, an election law expert at the University of California, Irvine, said states are getting much better at using voter information to fine tune their electoral maps. "Elected officials, armed with new data, are seeking maximum partisan advantage. And if the court doesn't put the brakes on it, this is likely to accelerate and get even worse."
This Supreme Court term will end in late June.
Pete Williams is an NBC News correspondent who covers the Justice Department and the Supreme Court, based in Washington.