How international (and other social) systems are stratified – how social positions are arranged in ranked relations of super-, sub-, and co-ordination – is obviously central to their structure and functioning. This chapter looks at two broad types of vertical differentiation: single (or convergent) hierarchies and heterarchies (or multiply ranked orders). I begin with a 2x2 typology of hierarchies, based on whether they are restricted to a single issue or institution and whether they have a single axis of stratification. Among multi-layer systems, which are the norm in international relations, I look at various types of “states systems,” which have different types of relations between more or less autonomous polities; “imperial” systems, which have a single axis of super- and subordination; and “heterarchies,” which have multiple axes of stratification. The chapter concludes by considering the distinctive ways in which typologies explain.