When the justices declined in October to review the string of victories same-sex marriage proponents had won in other parts of the country, it meant the number of states required to allow gay marriages grew dramatically, offering the kind of cultural shift the court often likes to see before approving a fundamental change.

The Michigan case now before the Supreme Court involves the issuance of marriage licenses to gay couples. The cases from Tennessee and Ohio concern whether states must recognize same-sex marriages performed in other states where such unions are legal. And Kentucky offers cases that touch on licensing and recognition.
In the 2013 case striking a key part of the Defense of Marriage Act, U.S. v. Windsor, the decision written by Justice Anthony M. Kennedy said the federal government could not refuse to recognize or provide benefits to people in same-sex marriages that were conducted in states where they were legal.

Dozens of lower-court judges nationwide have read Kennedy’s opinion — in which he was joined by Justices Ruth Bader Ginsburg, Stephen G. Breyer, Sonia Sotomayor and Elena Kagan — to mean that state bans violate constitutional rights as well.