This article addresses the iudicare limb of the grave breaches regime. While the Hague formula of aut dedere aut iudicare must certainly be considered when construing the iudicare limb of the grave breaches regime, this article shows that the iudicare limb applicable to grave breaches is independent of other similar conceptions. Moreover, we see that there is no absolute duty to arrest, nor can there be an absolute duty to prosecute and to punish. What the iudicare limb in fact entails is a duty to investigate and, where so warranted, to prosecute and to convict. In some circumstances, immunities influence this obligation. There are, in addition, certain implications arising from the procedural safeguards implicit in the iudicare limb. Finally, this article concludes with a word of caution concerning amnesties in hybrid accountability systems, querying whether international practice might slowly come to accept a less categorical regime, as it does in the field of war crimes committed in non-international armed conflicts and crimes against humanity. This would perhaps better reflect the political complexities of the transition from armed conflict to peace.