This contribution seeks to provide new conceptual configurations on Higher Education from a Latin America and European perspective. It reports on the results of an inter-institutional collaboration and interdisciplinary analysis of the processes and essential criteria for the accountability of the social responsibility of Higher Education. Our proposal aims at revising seminal concepts in the face of the current state of affairs of Higher Education, in the midst of a crisis of financial valuables and axiological values, and at a juncture where the States’ shrinking political power requires new social concepts for the development of Higher Education. The conceptual journey through the notions of relevance, equity, governance and equality proposes that universities gain new meaning as privileged spaces wherein horizons are broadened, knowledge is created and recreated, differences are respected, and gender is seen as both of essence and pervasive. The convergence of territorial uniqueness and interdisciplinary work allows for a cross-fertilization of current concepts, for example, by highlighting the intimate relationship between quality education and social justice, or by incorporating cognitive justice within a new model of the university.