Rather than consigning assemblages to the micro-politics of international relations, the chapter argues that assemblages can also be seen to play a role in the ‘grand’ structures of international relations. Structural IR theory normally only considers how subjects are ordered – hierarchically, anarchically, in core-periphery relations or in terms of networks. However, not only subjects but also assemblages – the bringing together of previously unconnected elements into novel constellations – play a critical role in structuring international relations. More specifically, one sub-category of assemblages – those constructed as malleable and governable which I call ‘governance-objects’ – is central to structure in international relations. The chapter begins with standard definitions of what structures are – patterns of interaction between elements – and briefly covers the range of models currently used to simplify different structures. Next the chapter points to the blindness of most structural theories of IR to the role of assemblages in general and governance-objects in particular. Thirdly, the idea that a polity is constituted precisely by the assemblage of a governance-object – the construction of something considered governable and worthy of governance – is advanced, suggesting that whereas anarchy is what states make of each other, a global polity is what actants render simultaneously governable and global.