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 State for Defence, a case challenging treatment by British troops of Iraqi civilians detained in Iraq. The Law Lords ruled that the Human Rights Act, adopted in 1998 to give internal effect to Europe's Convention on Human Rights and Fundamental Freedoms, has some, but not full, extraterritorial reach. The Lords relied most heavily on Banković v. Belgium, in which survivors of an air attack on Serbia applied to the European Court of Human Rights for redress against states that adhered both to the European Convention and the NATO treaty. The states denied the incident implicated their duty to guarantee rights "to everyone within their jurisdiction," as I've written:
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 a member 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.