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.

The Sustainable Development Goals (SDGs) constitute a working agenda for the international community with the aim of ensuring a better world for future generations. In this context, the development of competences related to SDGs is a challenge for Higher Education Institutions. Although there are several studies that address the relationship between SDGs and university teaching, the students’ knowledge about this subject has not been set out yet. In order to evaluate students’ knowledge, a questionnaire was designed, validated, and administered to students from different degrees. Statistical analysis showed a high reliability for the constructs (Smallest Cronbach’s Alfa = 0.859). The results showed interesting insights, either with descriptive analysis or inferential ones. For example, a low knowledge, in a general way, of SDGs was identified in the whole sample; significant differences between the scores obtained in professional and personal implications of SDGs were also detected and several differences arose between Health and Education students, the latter being more professionally involved with SDGs than the rest of the students.