The question “what is an international crime?” has two aspects. First, it asks us to identify which acts qualify as international crimes. Second, and more fundamentally, it asks us to identify what is distinctive about an international crime.Some disagreement exists concerning the first issue, particularly with regard to torture and terrorism. But nearly all states, international tribunals, and ICL scholars take the same position concerning the second issue, insisting that an act qualifies as an international crime if--and only if--that act is universally criminal under international law.This definition of an international crime leads to an obvious question: how exactly does an act become universally criminal under international law? One answer, the “direct criminalization thesis” (DCT), is that certain acts are universally criminal because they are directly criminalized by international law itself, regardless of whether states criminalize them. Another answer, the “national criminalization thesis” (NCT), rejects the idea that international law directly criminalizes particular acts. According to the NCT, certain acts are universally criminal because international law obligates every state in the world to criminalize them.This Article argues that if we take positivism seriously, as every international criminal tribunal since Nuremberg has insisted we must, the NCT provides the only coherent explanation of how international law can deem certain acts to be universally criminal.