This chapter moves from exploring the impact of complexity in the social sciences to examining its growing influence in policy and governance. It begins with a review of the attractions of orderly social science to the policy world and reviews some of the various forms that these have taken from New Public Management to Evidence-based Policy Making. It then goes on to explore the rise of ‘governance’ thinking as a way of reshaping conceptualisations of government and policy making and examines how this overlapped with the rise of complexity thinking and perspectives. The chapter concludes with a detailed but partial overview of the substantial emergence of complexity and policy-oriented research centres and the impressive growth of complexity-based research in most major areas of policy.