Scholars of global constitutionalism have recently come to examine international criminal law (ICL) and its associated institutions, in particular the International Criminal Court (the ICC). This article prolongs these efforts by pointing to and remedying two deficits of that project with particular emphasis on the Rome Statute crimes. First, how does one account for the role of the international trial in global constitutionalist terms? Second, can global constitutionalism insightfully explain the content and scope of these crimes – that is, both their substantive definition and the predominant modes of liability developed by the ICC? This article answers both questions affirmatively and offers an account of their nexus. It first shows that the Rome Statute crimes are often perpetrated through a hierarchically organized apparatus of control, and interprets their global constitutional significance via the principle of constituent power. It then makes use of Antony Duff’s relational account of criminal liability to offer an account of the international trial. In the international context, one can conceive of the trial as allowing state or state-like authorities to call each other to account, which renders justice to the core function of enabling and limiting political authority on which global constitutionalism centres.