The U.S. Supreme Court finished its most recent term on Friday. Several of its rulings addressed the powers of state courts, while others are likely to affect the cases landing on state dockets. Here are some of the highlights.

Probably the most significant case for state courts is one that didn’t have anything to do with them directly. In United States v. Skrmetti, the Supreme Court upheld Tennessee’s ban on gender-affirming care for minors, rejecting a claim that the law violated equal protection under the U.S. Constitution. Skrmetti involved a question of federal constitutional law coming out of federal court litigation. But by upholding Tennessee’s law, the Supreme Court created a federal rights vacuum. Following a pattern that we’ve seen in everything from abortion to property rights, litigants will increasingly ask state courts and state constitutions to fill the void.

We’ve already started to see state litigation challenging bans on gender-affirming care for minors. For example, a North Dakota trial court is expected to rule in the coming months on a lawsuit challenging a state ban. And in December, the Montana Supreme Court affirmed a preliminary injunction blocking that state’s ban, ruling that the law likely violated the state constitution’s express right to privacy. On the other side, the Texas Supreme Court last year upheld a state law banning certain medical treatments for transgender minors.

Skrmetti also bypassed a number of legal questions, most notably whether laws discriminating against transgender people should be subject to a heightened level of judicial scrutiny. Another thing to watch is whether litigants will now try to avoid a Supreme Court ruling on this question by shifting more broadly to state strategies for transgender rights.

Two other cases this term related to state courts more directly, reining in state judicial procedures to ensure compliance with federal law.

In Williams v. Reed, the plaintiffs had faced substantial delays from the Alabama Department of Labor in processing their benefits claims. They sued in state court, claiming violations of their federal due process and statutory rights. But the Alabama Supreme Court rejected their suit, concluding that under state law they first needed to go through the state’s administrative process — whose delay was the entire basis of their lawsuit — before filing suit in state court. The Supreme Court concluded that this catch-22 effectively immunized Alabama officials from lawsuits under the federal civil rights law at issue, Section 1983. In the face of that conflict, the Court explained, the state law was preempted by federal law and could not be applied by state courts.

The second case, Glossip v Oklahoma, was a high-profile death penalty appeal coming out of the Oklahoma Court of Criminal Appeals. After prosecutorial misconduct and withheld evidence came to light in Richard Glossip’s murder conviction, the state’s attorney general supported Glossip’s request to reopen his case and seek a new trial. But the court of criminal appeals, the highest criminal court in the state, ruled that his claims were procedurally barred under Oklahoma’s law governing post-conviction review.

Death penalty post-conviction cases like Glossip’s are notorious for procedural mazes and traps for the unwary that the Supreme Court has largely blessed. But here, the Court stepped in to stop the execution and order a new trial. The Court explained that it had jurisdiction to review Glossip’s case because, ultimately, the Oklahoma court lacked an independent and adequate state ground for its decision. The state court’s ruling, the Court explained, rested on an erroneous analysis of a Supreme Court case governing prosecutors’ knowing use of false evidence. The Court then looked at the evidence before it and the state attorney general’s own admission of error to conclude that a new trial was warranted. Glossip didn’t break much new ground by way of precedent, but it was significant because the Supreme Court so rarely intervenes in death penalty cases in the face of state procedural rulings.

I’ll conclude with one final case, Oklahoma Statewide Charter School Board v. Drummond, an expected blockbuster that fizzled. After an Oklahoma school board granted a charter to a Catholic school, the Oklahoma Supreme Court blocked the decision, ruling that the charter violated state law and the state constitution, as well as the U.S. Constitution’s Establishment Clause.