The essays collected in this special issue explore what legitimacy means for actors and institutions that do not function like traditional states but nevertheless wield significant power in the global realm. They are connected by the idea that the specific purposes of non-state actors and the contexts in which they operate shape what it means for them to be legitimate and so shape the standards of justification that they have to meet. In this introduction, we develop this guiding methodology further and show how the special issue’s individual contributions apply it to their cases. In the first section, we provide a sketch of our purpose-dependent theory of legitimacy beyond the state. We then highlight two features of the institutional context beyond the state that set it apart from the domestic case: problems of feasibility and the structure of international law.