Devolution has changed fundamentally the system of governance within the United Kingdom. The devolution of legislative and administrative competencies over a wide range of policies to Scotland and Wales necessitated the introduction of arrangements for policy co-operation and coordination involving UK Government and the devolved administrations. These arrangements are set out in concordats. In this article we consider why the concordats were necessary, and critically analyse their role as devices for maintaining coherence in, and legitimacy of, UK governance in the face of the challenges raised by devolution. We then extend our analysis of concordats to an examination of the role that sub-national authorities generally might play in multi-level governance systems. We do this by concentrating on the subsidiarity debate in EU governance, and consider whether this concept can be applied meaningfully to inform the structure of policy assignment in that multi-level governance system. The lessons gleaned from a study of UK devolution suggest that subsidiarity, while a potentially useful framework for assigning powers between national and supranational levels within a trans-national governance system, has little relevance when applied to the role of sub-national governance in trans-national systems.