The paper addresses the rising criticism to innovation policies that have assumed a direct and massive impact of universities in regional economies. It integrates the literature in economics of innovation, higher education, economic geography and regional studies. The paper shows why research excellence is considered a necessary condition for regional impact, why it is not sufficient, and whether there are substitutes. The Additional Material section includes an analysis, based on original data, on research excellence in universities in European peripheral regions. The policy implications call for a new approach to the role of universities.