A series of controversies that have structured the life of the International Criminal Court and which are often discussed separately can be traced to fundamental disagreements about the foundations of its authority. For some, the Court further crystalizes a sort of ius puniendi of the international community that is a direct continuation of the commitment to repress certain fundamental international crimes; for others, the key to the Court’s authority is, if anything, better understood as a function of sovereign delegation and agreement. The article explores the merits of these theories of both international criminal law and jurisdiction, both as theories and in light of the actual practices of international criminal justice. It may well be that an international ius puniendi can be said to exist in the abstract, and when it comes to core international crimes and the need to repress them. Even if the origin of some cardinal international criminal prohibitions is conventional, these prohibitions may have become so ingrained in the international legal order as to become inherent to it. But the public order and universal character of international crimes does not necessarily or easily translate to whatever particular institutions are devised to punish them. The article suggests, in this context, that on balance the practices of the Court are still better understood as a direct function of State consent. This is true when examining both the practice of the ICC towards non-States Parties and, crucially, towards States Parties. To see the Court as ‘merely’ the Court of its States Parties, however, is not to give up on the idea of universal repression, but to see it as mediated in practice by the complex agency of those States that pursue that aim.