Same-sex marriage
Same-sex marriage is a legally recognized marriage between two men or two women. It is accepted in many parts of the world, but is an extremely controversial issue in the United States. Some states have legitimized it, but, in general, it is intensely resisted by social conservatives. GLBT advocates, not surprisingly, consider its approval to be a fundamental right.
Defense of Marriage Act
At the Federal level, the Defense of Marriage Act, passed in 1996. Some Federal courts have overturned it on a district or circuit basis; it has not reached the Supreme Court of the United States. In some states where it was overturned, the state passed a constitutional amendment nullifying the court's interpretation.
Religious aspects
"Liberal religions", such as Reform Judaism or Unitarian Universalism, often will perform such ceremonies even without civil authority. It is opposed by Catholicism, Islam, and conservative Protestant denominations.