The social relevance of science has evolved significantly since the mid-twentieth century, leading to a change in the approach and development of the scientific activity. In this context, there has been a notable increase of in-depth studies addressing exchange and knowledge transfer processes between researchers and social agents, largely to encourage these processes from the scientific and institutional policies. This paper describes the evolution of the science-society relationships approaches and analyses the main elements of the exchange and knowledge transfer processes though an empirical study of the largest Spanish public research organisation. Results highlight that the dominant view on the relations between science and society is very limited and needs to be revised.