This chapter examines the material and mental aspects of four offences that are directly criminalized by international law: genocide, crimes against humanity, war crimes, and aggression. The discussions also cover some of the general principles of liability and defences that are of particular relevance to international crimes. Firstly, joint criminal enterprise, co-perpetration, command responsibility, and the defence of obedience to superior orders are considered. The chapter then looks at international and national prosecution of international crimes, including the Nuremberg and Tokyo Trials, the International Criminal Tribunals for former Yugoslavia and Rwanda, and the International Criminal Court. As prosecution is not the only, or predominant, response to international crimes, the chapter concludes with a discussion of alternatives and complements to prosecution, such as amnesties, and truth and reconciliation commissions.