Hierarchy-centered approaches to IR promise to deliver what anarchy-centered approaches have not: a framework for theorizing and empirically analyzing world politics as a global system rather than just an international one. At the core of this proposition are three features of hierarchical systems as they are represented across the growing IR literature on the topic. First, the structures of differentiation at the core of hierarchical systems are deeply implicated with power. Hierarchical systems are thus intrinsically political. Second, in world politics, hierarchies stratify, rank, and organize the relations not only among states but also other kinds of actors as well, and often even a mix of different actors within a single structure of differentiation. Third, there are many different kinds of hierarchical relations in world politics, each of which generate different “logics” influencing social, moral, and behavioral outcomes. Hierarchy has been understood in the IR literature in two ways: narrowly, as a relationship of legitimate authority; and broadly, as intersubjective manifestations of organized inequality. Hierarchy operates in a variety of different ways that range from ordering solutions to deep structures. We identify three such “logics” that have been fruitfully explored in IR scholarship and that can form the basis of a future research agenda: hierarchy as an institutionalized functional bargain between actors (a logic of trade-offs); hierarchy as differentiated social and political roles shaping behavior (a logic of positionality); and hierarchy as a productive political space or structure (a logic of productivity).