Why should a Spanish court take jurisdiction over an American lawyer accused of facilitating torture on Guantanamo Bay? What empowers a London magistrate to sign an arrest warrant for a former Chilean President? Can it be legitimate or morally defensible for an Israeli court to try a former Nazi whose crimes occurred outside Israel and indeed prior to the establishment of Israel? This book provides the first full account, explanation, and critique of extraterritorial punishment in international law. Extraterritoriality is deeply entrenched in the practice of legal punishment in domestic legal systems and, in certain circumstances, an established principle of public international law. Often, States claim the right to punish certain offences provided for under their own domestic laws even when they are committed outside their territorial boundaries. Furthermore, extraterritoriality is one of the most remarkable features of international criminal law. Many individuals have been prosecuted in different parts of the world for crimes against humanity, war crimes, genocide, etc. before tribunals which are often located outside the territorial boundaries of the state in which the offences were perpetrated. Finally, the issue of extraterritorial punishment is of pressing importance because of the emergence of new forms of globalized crime, such as transnational terrorism, drug-trafficking, trafficking of human beings, and so on. This book provides a convincing normative account of extraterritorial punishment. In doing so, it will steer current debates on international criminal justice and the philosophy of punishment in new directions, and link these debates to globalization, the emergence of transnational crime, terrorism, war, and the problem of impunity and mass atrocity.