The purpose of this paper is to understand the diverse rationales of the transformation of the University to respond to the challenges, evolutions and crises of the current global world, finding out what are the key aspects that articulate the discourses about its transformation. From a qualitative approach, the selected method was discourse analysis of interviews with 11 representative experts from different university cultures, sizes and World regions with senior experience in different kinds of transformation processes. The interviews explored the challenges and possible responses of universities and then were analysed to formulate 'the right questions of our time' on the transformation of the University in the global context. The results of the analysis allowed understanding the different meanings and levels involved as well as the motivations that are impelling the transformation of universities. Ten implicated tensions were also identified. The discussion is appropriate for substantiating the discourse on the transformation of the University, useful for the agents involved in it, as well as for understanding the prospective trends.