This article offers an analysis of the emerging scalar configuration of the governance of the European Union. It discusses how European integration stands for a move from a collection of territorially homogenous systems of rule towards a new assemblage of territories, authorities and rights. The paper first questions the stretchy territoriality of the seemingly obvious European level. Second it analyses the sectoral differences in the evolution of the width and the depth of integration, measured as the transfer of competencies to the EU level between the Rome Treaty (1958) and the Lisbon Treaty (200y). Third it turns to the day-to-day decision-making to assess the relations between players in EU governance and finally it looks more closely at the administrative wheels of the EU machinery.