The concepts, language and methods of complexity theory have been slowly making their way into international relations (IR), as scholars explore their potential for extending our understanding of the dynamics of international politics. In this article we examine the progress made so far and map the existing debates within IR that are liable to being significantly reconfigured by the conceptual resources of complexity. We consider the various ontological, epistemological and methodological questions raised by complexity theory and its attendant worldview. The article concludes that, beyond metaphor and computational models, the greatest promise of complexity is a reinvigoration of systems thinking that eschews the flaws and limitations of previous instantiations of systems theory and offers an array of conceptual tools apposite to analysing international politics in the twenty-first century.