But something could overshadow rulings in those high- profile cases: If Justice Anthony Kennedy were to use the court's last public session today to announce his retirement.
Kennedy has given no public sign that he would step down this year and give President Donald Trump his second high court pick in the first months of his administration.
Kennedy's departure would allow conservatives to take firm control of the court.
The justices today were expected to decide the case of Trinity Lutheran Church of Columbia, Missouri, which was excluded from a state grant programme to pay for soft surfaces on playgrounds run by not-for-profit groups.
Missouri has since changed its policy under Republican Gov. Eric Greitens so that churches may now apply for the money.
Also expected in the next few days, though there's no deadline by which the court must decide, was a ruling on whether to allow the administration to immediately enforce a 90-day ban on visitors from six mostly Muslim countries.
Justice Neil Gorsuch, Trump's first Supreme Court nominee, could play a pivotal role in both the travel ban and church playground cases.
If the eight justices are evenly divided, those cases could be argued a second time in the fall, with Gorsuch available to provide the tie-breaking vote.
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