Modern states have constructed a multiplicity of issue-specific regimes to facilitate collective action. The majority of these institutions are specific instances of the deeper institutional practices that structure modern international society, notably the fundamental institutions of contractual international law and multilateralism. Two observations can be made about fundamental institutions. First, they are “generic” structural elements of international societies. That is, their practice transcends changes in the balance of power and the configuration of interests, even if their density and efficacy vary. The modern practices of contractual international law and multilateralism intensified after 1945, but postwar developments built on institutional principles that were first endorsed by states during the nineteenth century and structured international relations long before the advent of American hegemony. Second, fundamental institutions differ from one society of states to another. While the governance of modern international society rests on the institutions of contractual international law and multilateralism, no such institutions evolved in ancient Greece. Instead, the city-states developed a sophisticated and successful system of third-party arbitration to facilitate ordered interstate relations. This institution, which operated in the absence of a body of codified interstate law, is best characterized as “authoritative trilateralism.”