The International Law Commission’s (ILC) draft articles on crimes against humanity contain some key provisions on the duty to establish national jurisdiction over crimes against humanity, under draft Article 7, and on the duty to investigate the possible occurrence of crimes against humanity, pursuant to draft Articles 8 and 9. This article analyses, first, the duty to establish national jurisdiction over crimes against humanity, focusing in particular on the identification of what constitutes ‘territory under a state’s jurisdiction’ and on the principle of universal jurisdiction. Secondly, it delves into the general duty to investigate situations in which crimes against humanity may have been committed, clarifying the circumstances in whic...