The European Union acts as a venue in which the EU member states enhance their problem-solving capacities when faced with issues having a cross-border or global dimension. Primary European Union law (‘the EU’s Constitution’) has served as a tool allowing for the adoption of a growing range of such European public policies. However, the EU’s constitution also occasionally acts as a constraint by not allowing for the adoption of certain political projects or steering them in a direction that does not correspond to the views of the (majority of) political actors. This constraining role is strengthened by constitutional overload (the sheer volume of norms of EU primary law) and constitutional inertia (the great difficulty of enacting revisions of the EU Treaties). As a response to these limits of the Union’s capacity to act, we have seen in recent years an increasing recourse to forms of flexible integration, and to unorthodox legal arrangements.