In the field of international law three core crimes generally make up the jurisdiction of international criminal tribunals: war crimes; genocide; and crimes against humanity. Only two of these crimes (war crimes and genocide) are the subject of a global convention that requires States to prevent and punish such conduct and to cooperate among themselves toward those ends. By contrast, there is no such convention dedicated to preventing and punishing crimes against humanity. An international convention on prevention, punishment and inter-State cooperation with respect to crimes against humanity appears to be a key missing link in the current framework of international law. The offence of crimes against humanity is a jus cogens and there is an erga omnes for states to prosecute and extradite offenders of crimes against humanity.This can be achieved by having international obligations founded on a specialised convention.