Sustainability, as a key concept in the education field, has submitted a relevant change during the last years. Thus, there is a growing debate about its meaning. It has undergone a crucial merging of significances from many fields: Ecology, environmental awareness, but also from politics, ethics or even spiritual approaches. All these fields have been co-involved in the building of such subject concept. In this sense, this article addresses the different ways of understanding sustainability as a polyhedral concept and how sustainability can be understood under the umbrella of the Sustainable Development Goals (SDGs). Furthermore, it is proposed a conceptual framework to teach this UN Program at Higher Education, contributing to the training of undergraduate and postgraduate students from both a professional and a personal point of view. This framework is applied in a case study-in particular, in a course of Primary Teacher Degree called Didactics of Matter and Energy. This article finishes with practical consideration to build a change-maker University.