1. MCA § 7 denies the federal courts jurisdiction to hear habeas actions, like the instant cases, that were pending at the time of its enactment.
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2. Petitioners have the constitutional privilege of habeas corpus. They are not barred from seeking the writ or invoking the Suspension Clause’s protections because they have been designated as enemy combatants or because of their presence at Guantanamo.
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(c) The Suspension Clause has full effect at Guantanamo. The Government’s argument that the Clause affords petitioners no rights because the United States does not claim sovereignty over the naval station is rejected.
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3. Because the DTA’s procedures for reviewing detainees’ status are not an adequate and effective substitute for the habeas writ, MCA § 7 operates as an unconstitutional suspension of the writ.
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4. Nor are there prudential barriers to habeas review.
Id., syllabus at 2–8 (not a binding statement of the holding).
More later; my initial observation is only that it's a shame this is a not-unexpected 5–4 decision (the real issue being whether it would go for or against the prisoners)... and that Justice Scalia, in particular, knows almost nothing of military history, either of the US or in general.