In an epoch of transnational armed conflict, global environmental harm, and rising inequality, the extraterritorial application of human rights law has become a pressing and controversial legal issue. Human rights are invoked to address a number of global-scale problems, such as trans-border environmental harm, social and economic development, global inequality, the repression of piracy in ungoverned spaces, and military occupation and armed conflict in the territory of a third state. The chapters collected in this volume grapple with the promise and the dilemmas of the extraterritorial application of human rights law through an analysis of the legal, theoretical, and practical questions raised by extending states' human rights obligations beyond their national territories.