Technology transfer or knowledge exchange? Which one of the two expressions better identifies the possible modes of interactions between Universities, market and firms? The paper addresses this question in the light of the advancements in the economic literature on the topic. It emerges that channels of interaction go far behind the technology transfer, including traditional output of university - scientific publications and graduates - and a variety of channels ranging from research in cooperation to consultancy. Moreover, it emerges that different channels are often complementary: a fact that has important implications for innovation policies and university long term strategies. The problem of the possible negative feed back of cooperation with private entities on production of open science by academics and on the traditional role of universities is the main concern of a growing stream of literature. Until now the results point, in a large majority, to a complementarity between academic research and market activities. Nonetheless, given the heterogeneity of academic production, and the possible different kinds of production functions, the conclusion can not be easily generalized.