Drawing on various disciplinary and scholarly approaches to the multiple roles of higher education in society, this paper offers a new conceptualisation of the non-economic contributions of higher education. The conceptual model identifies two basic dimensions in higher education's contributions to society. The first, axiological dimension pertains to the objects of higher education: what higher education does, what is in the centre of its activities. This includes three key elements: knowledge/skills (basic and applied knowledge, generic and particular skills), norms and values (social, cultural, professional, civic) and social value (social statuses). The second, praxeological dimension pertains to the internal dynamics of higher education: what higher education does in relation to the object, the processes, practices, activities. This entails three: transmission, transformation and creation. The resulting model combines the two dimensions (axiological and praxeological), identifying nine key domains of the contributions of higher education to society. This conceptualisation both brings together the three major components of higher education's role and attends to its internal dynamics. It illuminates the intrinsic value of teaching, learning and research and the inherent transformative potentials of higher education for individuals and for societies. It embraces actual and potential contributions of higher education to society. It is applicable at both individual and collective levels. It works on the scales of group, institution, local, national and global.