The ongoing reallocation of wealth and power from the West to the "rising rest" promises to produce a new pecking order over the course of the next few decades. Although there is a well-developed body of knowledge on the material dimensions of power transitions, existing scholarship provides a much more embryonic intellectual foundation on the normative dimensions of international change. Transitions in the international distribution of power produce not only novel hierarchies, but also novel brands of international order that rest on the social and ideological proclivities of newly powerful states in the system. This article explores the normative dimensions of hegemony by examining the geopolitical, socioeconomic, cultural, and commercial logics that inform different orders. The normative foundations of hegemony are studied across four great powers: the Ottoman Empire, Imperial China, Great Britain, and the United States. The cases reveal that as great powers rise, they as a matter of course seek to push outward to their expanding spheres of influence the norms that provide order within their own polities. Accordingly, today's emerging powers will not embrace the existing international order erected during the West's watch. On the contrary, China and other rising powers will seek to fashion alternative orders based on their own cultural, ideological, and socioeconomic trajectories. If the next international system is to be characterized by a rules-based order rather than competitive anarchy, it will require a new normative consensus that rests on toleration of ideological and political diversity.