This paper describes the university social responsibility trends that Higher Education Institutions and Universities from around the world are implementing, whether public or private. The aim of this study is to identify the categories of Social Responsibility that are assuming institutions and what approaches and strategies are developed. Theoretical research was conducted under the methodology of systematic review based on the PRISMA strategy in a range of ten years from 2003. The results show a tendency to humanistic, pedagogical, ethical and socio-curricular approaches, with a variety of strategies for different actors.