Scholars tend to think of international relations as taking place in a world of anarchy -- a decentralized system in which sovereign states are the masters and rulers of their realm. But much of the globe has historically been a world of hierarchy, where powerful states build order and weaker states submit to it. This is the world of empires, tributary systems, hegemonic orders, spheres of influence, and patron-client relations. In this pioneering work, Lake argues that hierarchical relations are best seen as bargained relationships in which the dominant state provides "services" -- such as order, security, and governance -- to subordinate states in return for compliance. What distinguishes the various forms of hierarchy, from colonialism to modern alliances, is the amount of sovereignty signed over to the leading state. Lake uses this insight to explore patterns of U.S.-led hierarchy in the security and economic realms, relying on measures such as the presence of U.S. military bases, exchange-rate linkages, and trade dependence. The danger in this sort of work is that it is easy to confuse willing subordination with coercion. Lake argues that because some states -- both small and large -- are subordinate to the United States and others are not, hierarchy is based on voluntary "contracts," not just power. His theory does not illuminate hierarchies that are a mix of coercion and consent, but it offers new thinking about the complex interactions between the United States and its junior partners.