University quality is an essential category to analyze higher education and to approach its transformation. Nonetheless, conceptualizing quality is still a pending task, which requires, simultaneously, a new concept of university. It is essential to know what type of university we have and what type we need in Latin America. The article displays a typology of existing universities in this continent: professionalizing, research-oriented, entrepreneurial, corporative, developmental, and socialist -as is the case in Venezuela. Within the framework of this typology, we describe the forces that push for a new concept of university and discuss the impossibility of offering a single concept of quality that is able to encompass all of the universities which we have and those which we need. As a contribution to the design of different concepts of quality, we set out a heuristic model to undertake the re-conceptualization of the Latin American university; one which counteracts the tendency to standardize the university into a single ideal type to which all existing ones must look forward. Each university model demands a specific concept of quality; therefore it is imperative to build as many systems of indicators as types of universities could emerge.