For the past 25 years, the EU has undergone a process of incremental constitutionalisation and institutional reform - recently culminated in the Lisbon Treaty. Different treaty reforms have addressed specific institutional shortcomings, so that today’s executive and legislative functions are distributed among the European Parliament, the European Council, the Council of Ministers and the European Commission. Still, the EU remains short of what is generally referred to as a government. The elected political leadership of a state’s executive branch is often the most visible, recognised and scrutinised part of a constitutional system. Thus, I argue that the EU’s constitutionalisation process, driven no less by national governments, has set-up an effective judiciary and legislature but has failed to provide the EU with a clearly identifiable executive. Even in the post-Lisbon EU, executive leadership, executive visibility and executive accountability is only very sparsely provided by the Commission and the European Council. This paper examines the legal and political reasons behind this Montesquieuian shortcoming. In doing so it focuses on the EU’s relevant political particularities and constitutional restraints, thus, explaining why the European integration process has not lent itself to create an EU executive in the Montesquieuian sense. Based on this analysis, I argue that the Union’s executive opacity is explainable. However, if the EU is to continue its process of incremental constitutionalisation, a restructuring if not a reinvention of its executive branch is paramount.