•The paper builds a comprehensive review of the current research on the Third Mission of universities and offers an innovative framework of measures to support the enactment of the Third Mission.•The Third Mission represents the economic and social mission of the university and its contribution to communities and territories.•Policy makers and university managers should avoid isomorphism, or rather, the tendency to emulate “world class” universities.•University-Industry labs can bridge the gap between university and society at large.•Social sciences and humanities facilitate both understanding of the complexity of the economic, social and environmental issues involved, and generate collaborative strategies between university-industry labs.•A continuous process of entrepreneurial discovery and exploration of market opportunities can foster collaboration between university-industry-government. In recent years, there has been increasing pressure on Universities to shift from focusing primarily on teaching and performing research, and to add an equivocal Third Mission (TM), labelled “a contribution to society”. Unprecedented challenges have been redesigning the missions of Universities, which are often perceived as being at a crossroads. The TM is a multidisciplinary, complex, evolving phenomenon linked to the social and economic mission of Universities in a broad sense. Existing studies mainly focus on Universities in accomplishing their traditional missions, or they offer a narrow perspective of the TM. To the best of our knowledge, no systematic literature review has been performed on the TM to comprehensively explore its heterogeneous functions, constraints, clashes and incorporation within education and research. This paper presents a systematic review of the state of knowledge and develops a novel framework for the enactment of the TM. The paper reveals the potential and the constraints of the recurring themes of the TM, focusing especially on the engagement of non-academic stakeholders. It also suggests, to scholars and policymakers, a selection of measures through which some of the challenges might be faced. The paper offers both a descriptive and a thematic analysis, through examination of 134 peer-reviewed articles which were published between 2004 and May 2019.