Can a state exercise criminal jurisdiction today for World War II war crimes, on the basis of a universal jurisdiction statute adopted in 1991? This is a question of retroactive state criminal jurisdiction, that is, the exercise of criminal jurisdiction on the basis of rules adopted subsequently to the time of the commission of the offence. The article assesses the complications arising from the intersection of time, state criminal jurisdiction and human rights under international law from the perspectives of the principle of legality, extradition law and the duty to prosecute past human rights violations. It concludes that in principle retroactive state criminal jurisdiction is permissible under international law. However, domestic legal standards may well vary and preclude it so as to offer a higher standard of protection for the accused, provided that they remain compatible with a state's eventual treaty-based duty to prosecute.