Unpacking the role of universities in the emergence, development and impact of social innovations - A systematic review of the literature

•Internal and external demands are growing for universities to integrate social innovation in their three missions.•Literature on university third mission socially-oriented activities is conceptually well developed and a growing field.•Studies on impact of social innovation in university teaching, research and outreach are scarce.•Studies addressing institutional change and incentive structures that influence university social innovation are limited.