University Social Responsibility (USR) has been consolidated in recent decades as the management's paradigm of XXI the century university (Vallaeys, 2014; Coppa, 2011; Villar, 2009). There are many works that have tried to approximate a general definition; others have analyzed the implementation of RSU initiatives in different contexts, as a contribution to their interpretation and study; and some more have proposed evaluation schemes of the perceptions and practices of USR in Institutions of Higher Education (HEI) of different latitudes. This paper examines the advances in the evaluation of USR because of its importance for self-diagnosis and the generation of continuous improvement processes in the missionary functions of education, research, internationalization, and extension. Based on the systematic literature review (SLR) and content analysis, a summary of the most relevant publications is presented, highlighting the most representative meeting points. There were identified as main trends the use of perception questionnaires, the adaptation of the GRI indicators and the analysis of reports, web pages and management reports. Finally, conclusions are offered about the state of knowledge and some recommendations for the development of new research in this field. Keywords: University Social Responsibility; assessment; auto diagnosis.