Despite the deeply contested nature of international criminal law (ICL), there is almost complete scholarly agreement concerning the nature and consequences of international criminalization. Almost all ICL scholars view an international crime as an act that is directly criminalized by international law itself, making domestic criminalization irrelevant. And almost all ICL scholars believe that, because international law is superior to domestic law, international criminalization imposes significant limits on states’ ability to tolerate impunity. This chapter challenges both ideas. It begins by demonstrating that positivism is incapable of establishing either direct criminalization law or the consequences that supposedly follow from it. The chapter then provides an alternative definition of an international crime – as an act that international law obligates all states to criminalize and prosecute – that not only has a stronger positivist foundation than direct criminalization, but also better explains direct criminalization’s supposed consequences.