Partial Birth Abortion Ban Upheld, But on Narrow Ground:
The opinions are here. As expected, Justice Kennedy wrote the opinion for the Court. Based on a quick skim, it looks like a very narrow opinion: the Court distinguished but did not overrule Stenberg v. Carhart, and upheld the federal statute under the Casey plurality "undue burden" test. The Court also left open the possibility of an as-applied challenge to the statute at a later date. The majority opinion was joined by Roberts, Scalia, Thomas, and Alito. Thomas wrote a short concurrene joined by Scalia. Ginsburg wrote the dissent joined by Stevens, Souter, and Breyer.

  Notably, the court assumed rather than decided that the Casey "undue burden" test applied. Justice Kennedy noted that Thomas and Scalia had not agreed with that test, but reasoned that even under it the law would be upheld. Thomas's very brief concurrence, joined by Scalia, states that he joins the majority because it's faithful application of Casey — but that he would want to overrule the line of cases. He also notes that there was no Commerce Clause challenge brought to the law, and that it might face such a challenge later (Aside: Might there be a Thomas-Ginsburg-Stevens-Souter-Breyer majority for that?). Roberts and Alito did not write separately, so we don't know much about where Roberts and Alito will come out beyond the facts of this particular case; they could be anywhere from Kennedy's position on one end to Thomas and Scalia's position on the other.

  Justice Ginsburg's dissent is pretty heated, in some places almost Scalia-esque. She contends the majority's opinion is "irrational," and "cannot be understood as anything other than an effort to chip away" at abortion rights. She writes:
Today’'s decision is alarming. It refuses to take Casey and Stenberg seriously. It tolerates, indeed applauds, federal intervention to ban nationwide a procedure found necessary and proper in certain cases by the American College of Obstetricians and Gynecologists (ACOG). It blurs the line, firmly drawn in Casey, between previability and postviability abortions. And, for the first time since Roe, the Court blesses a prohibition with no exception safeguarding a woman’s health.
  Also interesting -- at one point, Justice Ginsburg also accuses the majority of having a "way of thinking" that "reflects ancient notions about women'’s place in the family and under the Constitution— --ideas that have long since been discredited." (This accusation is followed by a "compare" string, comparing the rhetoric of Supreme Court opinions 100 years ago to language in one opinion Ginsburg wrote and another that she successfully argued.)

[Note to readers: I'll just add to this post as I read more of the opinion during the morning.]