Update: An earlier version of this story incorrectly attributed a quote from the president of Freedom to Marry.

After years of legislative and political victories, supporters of same-sex marriage are running out of states where friendly politicians can deliver on legislation legalizing unions between gay and lesbian couples. So marriage equality supporters are shifting tactics, focusing on courts of law rather than state legislatures.

In at least 15 states, same-sex couples have brought lawsuits aimed at getting their unions recognized. The cases fall into three broad categories: One set seeks to overturn state bans on same-sex marriage. Another seeks to force states to recognize marriages that occurred in other states. And a third deals with some of the less romantic aspects of marriage, like divorce.

“We all, as a movement, recognize that we got to where we are in terms of marriage equality by pursuing all avenues,” said Brian Moulton, the legal director at the Human Rights Campaign. “There are some more places — Illinois, Hawaii, New Jersey — where we may be able to advance marriage through the state legislatures, but beyond that there are a lot of states that have constitutional amendments that are going to have to be rolled back by a popular vote” or by the courts.

In the months after a Supreme Court ruling striking down key elements of the Defense of Marriage act, the courts have been the venue of choice for backers of same-sex marriage.

On Friday, a court in Santa Fe County, N.M. ruled the county could issue same-sex marriage licenses. A judge in Albuquerque is expected to rule on a lawsuit brought by half a dozen same-sex couples that could legalize marriage throughout the state.

Across the border in Texas, the state Supreme Court said Friday it will schedule oral arguments for Nov. 5, on whether two gay couples that were married in other states can get divorced. One couple was granted a divorce in February 2010, in Austin; a court in Dallas granted another couple a divorce in 2009. Texas Attorney General Greg Abbott (R) filed motions to intervene in both cases, saying state law both prohibits same-sex marriage and prohibits any legal recognition of those marriages — which includes granting a divorce.

Earlier this month, three gay couples in Tennessee filed suit seeking to overturn their state’s same-sex marriage ban. In Cincinnati, a federal judge ruled that a dying man could be listed as married on his death certificate after he and his partner were married in Maryland last month. Jim Obergefell will be listed as the surviving spouse when his partner, who suffers from Lou Gehrig’s disease, passes away, the Associated Press reported.

A couple in Louisville filed suit last month to overturn Kentucky’s ban. A New Orleans couple filed a lawsuit seeking to force Louisiana to recognize their marriage after they traveled to Iowa, where same-sex unions are legal. Lawsuits are also pending in Arkansas, Illinois, New Jersey, Pennsylvania, Nevada and Virginia.

The most bizarre case involves a couple in Kentucky, where one partner is trying to use the state’s spousal privilege law to avoid testifying against the other, who is accused of murder. Prosecutors say the privilege law doesn’t apply to the couple, because they are not legally married; lawyers for the defendant and her partner say the amendment to the state constitution banning same-sex marriage is unconstitutional, and thus the two should be treated as married. The trial is scheduled to begin Friday.

The lawsuits highlight the different interpretations of a U.S. Supreme Court opinion issued earlier this year that struck down the heart of the Defense of Marriage Act, the 1996 law that defined marriage as solely between a man and a woman. The decision, in United States v. Windsor, declared the prohibition on federal recognition of legally married couples unconstitutional.

Backers of same-sex marriage say the court’s opinion opens the door for challenges to existing bans. Supporters of the bans, though, say the Court left it up to the states to decide how to define marriage, and whether to ban unions between same-sex couples.

“The people of Texas have the same right as the people of Massachusetts or New York to have a voice in shaping their state’s destiny,” Abbott, the Texas Attorney General, said in a brief to the state court, according to the Austin American-Statesman. “And Texans have spoken clearly. Their voice commands that only the union of one man and one woman will be recognized as a marriage in Texas.”

The court cases reflect the political reality that same-sex marriage backers don’t have many avenues for legislative advancement. Of the 14 states where Democrats control both chambers of the state legislature and the governor’s mansion, same-sex marriage is legal in nine, and another four permit civil unions (Socially conservative West Virginia is the lone Democratic state that has not allowed same-sex unions).

Beyond those blue states, same-sex marriage backers have had trouble winning over Republican supporters. Only one legislative chamber controlled by Republicans — the New York state Senate — has voted to pass a same-sex marriage bill. That leaves backers of marriage equality searching for new paths.

“Martin Luther King, Jr. spoke of the many ‘methodologies of social change,’ all legitimate parts of the American system,” said Evan Wolfson, president of the pro-gay rights Freedom to Marry. “We are employing all of them — litigation, legislation, ballot measures, public engagement and direct action.”