The aim, and the very raison d'être, of the law of jurisdiction has historically been to legally delimit spheres of State power and prevent international conflict from arising. In the classic view, the international law of jurisdiction aspires to prevent global chaos flowing from different States applying their own laws to one and the same situation. In a world characterized by increasing interdependence and multiple identities, the normative force of this ordering goal may not have run out of breath. Concurrently, however, a law of jurisdiction that limits itself to keeping States at arm’s length from each other may fail to recognize that States have adopted common substantive norms and have set joint goals, for whose actual realization the international community may crucially depend on unilateral action. The limits of such action in the global interest are a key challenge for a modern law of jurisdiction.