Many scholars now argue for deemphasizing the importance of international anarchy in favor of focusing on hierarchy – patterns of super- and subordination – in world politics. We argue that only one kind of vertical stratification, governance hierarchy, actually challenges the states-under-anarchy framework. But the existence of such hierarchies overturns a number of standard ways of studying world politics. In order to theorize, and identify, variation in governance structures in world politics, we advocate a relational approach that focuses on three dimensions of hierarchy: the heterogeneity of contracting, the degree of autonomy enjoyed by central authorities, and the balance of investiture between segments and the center. This generates eight ideal-typical forms: national-states and empires, as well as symmetric and asymmetric variants of federations, confederations, and conciliar systems. We argue that political formations – governance assemblages – with elements of these ideal types are likely ubiquitous at multiple scales of world politics, including within, across, and among sovereign states. Our framework suggests that world politics is marked by a heterarchy of nested and overlapping political structures. We discuss broad implications for international-relations theory and comparative politics, and illustrate our approach through an analysis of contemporary China and the evolution of the British ‘Empire’ in the 19th and 20th centuries.