The jurisdictional framework governing the prosecution and punishment of international crimes is unusual. While the prosecution of domestic crimes is ordinarily limited to the courts of states with a connection to the offence or offender, such connections are not required in the context of international criminal punishment. Those accused of international crimes (such as crimes against humanity or war crimes) can be tried before the courts of foreign states that are unconnected to the offence, or before international tribunals. In this talk, I examine how this reality raises the question of whether the international criminal law framework and the unique scope of the right to punish it entails can be justified. I examine the shortcomings of existing theories of what might justify international criminal punishment. I also begin to sketch out a new theory, grounded in an historical account of the field, highlighting the connection between parallel changes in ideas of state sovereignty and the definition of international crime over recent centuries.