Regional development is one of the main EU spending priorities through its Cohesion Policy. Brexit is among several influences on the future of the policy, whose evolution is part of a wider reshaping of the principles and practice of regional policy in Europe. In the context of emerging policy challenges and recent contributions to the regional policy literature, the article highlights innovation, human capital and effective institutions as three crucial dimensions of future policy. It argues that a shift in regional policy priorities, governance and territorial focus is underway – partly influenced by place-based policy thinking - at EU level under Cohesion Policy as well as under national regional policies in the EU27 and the UK