The aim of this article is to reflect upon the emergence of the "third mission" of universities as a critical (but not new) dimension of university activities. It recalls the role of our changing understanding of knowledge diffusion and circulation in its growth. It then focuses on the four main lessons derived from the analysis of the different dimensions of the so-called "third mission" to underline the tensions generated with the other missions. This leads us to suggest a move from three missions to three functions that articulate differently the three missions: mass tertiary education, professional specialized higher education and research and academic training. Each university is then characterized by the specific mix (inherited and/or constructed) of these three functions.