This introductory article sketches the problématique of this special issue on ‘Subsidiarity in the European Union and beyond’. It starts with a short historical overview of the origins, meanings and implementation of the subsidiarity principle within the EU. Subsequently, it problematizes the concept and application of subsidiarity in a multilevel governance context by examining two fundamental characteristics of this essentially contested concept that render it fascinating to study: its complexity and power-relevance. The relatively new concept of global subsidiarity is briefly discussed to situate the intra-EU discussion in a wider context. This introduction ends by discussing some of the findings of the special issue’s two substantial articles – that both deal with policy topics in which different competence regimes meet – in light of the subsidiarity problématique.