With the creation of the European Higher Education Area, universities are undergoing a significant transformation that is leading towards a new teaching and learning paradigm. The competencies approach has a key role in this process. But we believe that the competence approach has a number of limitations and weaknesses that can be overcome and supplanted by the capabilities approach. In this article our objective is twofold: first, make a critical analysis of the concept of competence as it is being used in higher education, identifying its limitations and weaknesses; and second, present the potential of the capabilities approach for higher education and review its complementarity to the competence approach. We begin with a brief characterisation of the capabilities approach and its implications for education. Then we examine some implications of the competencies approach in higher education and the reasons that led us to choose the DeSeCo proposal for comparison with the capability approach. We then go on to compare the two approaches, addressing 1) the aims of education and 2) the concept of competence and capability. Finally, we address the implications of incorporating the capabilities approach in learning and teaching in higher education.