Here, in a nutshell, are the marriage equality rulings issued just now by the U.S. Supreme Court, with links to the actual judgments:

► Judgment in United States v. Windsor: By a 5-4 vote, the Court held that equal protection and due process guarantees inherent in the Due Process Clause of the 5th Amendment to the Constitution forbid the federal government to privilege one class of married people over another, as the Defense of Marriage Act had required. The Act is thus unconstitutional as applied to same-sex couples married in states permitting such marriages. (Prior post.) Quote from opinion for the Court by Justice Anthony M. Kennedy (pp. 25-26):

‘DOMA instructs all federal officials, and indeed all persons with whom same-sex couples interact, including their own children, that their marriage is less worthy than the marriages of others. The federal statute is invalid, for no legitimate purpose overcomes the purpose and effect to disparage and to injure those whom the State, by its marriage laws, sought to protect in personhood and dignity. By seeking to displace this protection and treating those persons as living in marriages less respected than others, the federal statute is in violation of the Fifth Amendment. This opinion and its holding are confined to those lawful marriages.’

► Judgment in Hollingsworth v. Perry: By another 5-4 vote, the Court held that petitioners, private parties opposed to same-sex marriage who stepped in when the State of California would not, did not have standing. The petitioners had appealed a federal district court ruling that invalidated Proposition 8, the state constitutional provision banning gay marriage. Quote from opinion for the Court by Chief Justice John G. Roberts, Jr. (p. 17, citations omitted):

‘The Article III requirement that a party invoking the jurisdiction of a federal court seek relief for a personal,particularized injury serves vital interests going to the role of the Judiciary in our system of separated powers.“Refusing to entertain generalized grievances ensures that . . . courts exercise power that is judicial in nature,” and ensures that the Federal Judiciary respects “the proper — and properly limited — role of the courts in a democratic society.” States cannot alter that role simply by issuing to private parties who otherwise lack standing a ticket to the federal courthouse.’

This ruling leaves in effect the lower court order allowing same-sex marriages in California. SCOTUS blog posts on the question here.