Most EU-scholars conceive of the EU as a multilevel polity with strong powers to regulate economic policy externalities among the member states but little power to intervene in, let alone assume, core functions of sovereign government (core state powers) such as foreign and defense policy, public finance, public administration, and the maintenance of law and order. This book challenges this view. Based on a systematic comparison of integration processes in militarysecurity, fiscal policy, and public administration, it finds steady progress in the integration of core state powers although with substantial sectoral variation. But the EU is not heading towards state-building. In contrast to the historical experience of national federations, the Europeanintegration of core state powers proceeds mostly by regulating national capacities, not by creating European ones, and leads to territorial fragmentation rather than increased cohesiveness.