Somewhere in between unipolar and imperial orders, hegemonies divide the continuum from anarchy to hierarchy in world politics, connoting interstate systems of the highest concentration of authority. However, depending on the author, hegemony might denote the concentration of relative capabilities in a single state, the presence of a state that seeks international leadership, general consent in the international society regarding subordination to a central order, or a combination of these phenomena. Similarly, scholars debate the extent to which the relation of authority entailed by hegemony should encompass the economic, military, and/or ideational domains. Given this multiplicity of meanings, this review of extant definitions illuminates some issues that must be addressed explicitly when dealing with this concept. Although hegemony might mean different things for different intellectual traditions, these understandings are interconnected in a family resemblance structure that has facilitated mutual intelligibility. A mapping of this network of meanings suggests that special attention needs to be paid to how scholars have thought about the capabilities that would-be hegemons have, the roles they play, and the type of response they elicit from subordinate states. It also suggests the economic, military, and ideational dimensions of hegemony should be explicitly considered in theoretical discussions. Finally, it highlights the importance of avoiding ambiguity by connecting theory with empirics and providing clear measurement strategies. Measurement is essential to delineate the geographical and temporal scope of hegemonies with more precision, to compare them, and to evaluate their effects on certain outcomes. Debates about hegemony have undergone important empirical progress throughout the decades rendering this a promising area for future research.