Ideas about the nature of international order have been central to the contest between Russia and 'the West' in the twenty-first century and are fundamental to the relationship between Russia and the structures and states of the European Union (EU). The extent to which this order is, or should be, a liberal one is the source of much political and analytical debate in the EU-Russia landscape, as is the nature of the role of the United States (US) in both international and European politics and security. In the context of a more assertive Russian foreign policy, a rising China and a closer Sino-Russian relationship, and difficult Russia-US relations, the EU is increasingly entangled in the net of Russia's relations with others, especially the US. This chapter begins by considering the idea of a liberal world order (LWO), its origins, and some of the most significant debates about its character. Intimately connected to these debates are the issues of the LWO's Cold War origins and its relationship to US hegemony. It explores Russia's relationship to the LWO, and the ways in which that relationship is informed by Russian governmental concerns with US hegemony, or unipolarity. The chapter then considers the complex interrelationship of Russia, the LWO and Europe before concluding with some thoughts about possible futures.