From the outset, European integration was about the transfer of powers from the national to the European level, which evolved as explicit bargaining among governments or as an incremental drift. This process was reframed with the competence issue entering the agenda of constitutional policy. It now concerns the shape of the European multilevel polity as a whole, in particular the way in which powers are allocated, delimited and linked between the different levels. This Living Review article summarises research on the relations between the EU and the national and sub-national levels of the member states, in particular on the evolution and division of competences in a multilevel political system. It reviews normative reasons justifying an appropriate allocation of competences, empirical theories explaining effective structures of powers and empirical research.The article is structured as follows: First, normative theories of a European federation are discussed. Section 2 deals with legal and political concepts of federalism and presents approaches of the economic theory of federalism in the context of the European polity. These normative considerations conclude with a discussion of the subsidiarity principle and the constitutional allocation of competences in the European Treaties. Section 3 covers the empirical issue of how to explain the actual allocation of competences (scope and type) between levels. Integration theories are presented here in so far as they explain the transfer of competence from the national to the European level or the limits of this centralistic dynamics. Moreover, we include empirical studies on the effective vertical allocation of powers in the EU.Normative and empirical theories reveal that most powers are sharing rather than separated between levels. Therefore, article therefore concludes that politics and policy-making in the EU have to be regarded as multilevel governance. In Section 4, we summarise the main theoretical approaches and findings from empirical research on European multilevel governance. In the conclusion, we sketch some suggestions for further discussion and research in the field (Section 5).