According to the received view crimes like torture, rape, enslavement or enforced prostitution are domestic crimes if they are committed as isolated or sporadic events, but become crimes against humanity when they are committed as part of a ‘widespread or systematic attack’ against a civilian population. Only in the latter case can these crimes be prosecuted by the international community. One of the most influential accounts of this idea is Larry May’s International Harm Principle, which states that crimes against humanity are those that somehow ‘harm humanity.’ I argue that this principle is unable to provide an adequate account of crimes against humanity. Moreover, I argue that the principle fails to account for the idea that crimes against humanity are necessarily group based. I conclude by suggesting that the problem with May’s account is that it relies on a harm-based conception of crime which is very popular, but ultimately mistaken. I submit that in order to develop an adequate theory of crimes against humanity we need to abandon the harm-based model and replace it with an alternative conception of crime and criminal law, one based on the notion of accountability.