The question's occupied U.S. courts for half a century, as our colleague Kal Raustiala recently wrote, and it lurks beneath the surface of much of the post-9/11 executive detention litigation.
The House of Lords weighed in yesterday in Al-Skeini and others v. Secretary of S
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According to "‘the ordinary and well-established meaning ... in public international law,’" states argued, jurisdiction "‘involves the assertion or exercise of legal authority, actual or purported, over persons owing some form of allegiance to the State or who have been brought within that State’s control,’" and "‘generally entails some form of structured relationship normally existing over a period of time.’" The Court agreed that Convention obligations ordinarily apply only within amember state’s territory; therefore, it rejected the application. Yet it reaffirmed its authority in exceptional cases to review a state’s exercise of extraterritorial jurisdiction. Such exceptions might occur when a state, "through the effective control of the relevant territory and its inhabitants abroad as a consequence of a military occupation or through the consent, invitation or acquiescence of the Government of that territory, exercises all or some of the public powers normally to be exercised by that government," the Court wrote, or when a state acts outside its territory pursuant to international law. It indicated that judicial review would be particularly appropriate when necessary to avoid stranding applicants in a "vacuum in human rights’ protection."
Based on similar reasoning the Law Lords extended Human Rights Act protections to 1, but not all 6, of the Iraqi claimants; lawyers in the latter cases say they'll now press their claims before the Strasbourg Court.