Purpose: The purpose of this paper is to study how experts on teaching sustainability in engineering education contextualize sustainability; also to evaluate the understanding of sustainability by engineering students. The final aim is to evaluate what pedagogy experts believe provides better opportunities for learning about sustainability in engineering education. Design/methodology/approach: The authors used conceptual maps (cmaps) analysis with two taxonomies of four and ten categories. The first taxonomy clusters the significance of sustainability in environmental, technological, social and institutional aspects and shows the main trends; the second (of ten categories) divides the previous categories into greater detail. To evaluate the experts' cmaps two indices were defined that provide information about what experts think sustainability is most related to and evaluate how complex they see the sustainability concept. In total, 500 students from five European engineering universities were then surveyed and the results compared with those of the experts. Finally, interviews were held with experts to try to determine the best pedagogy to apply to achieve learning around sustainability. Findings: The results show that Engineering Education for Sustainable Development (EESD) experts consider that institutional and social aspects are more relevant to sustainability than environmental and technological ones. The results were compared with the understanding of sustainability by a sample of more than 500 engineering students who had taken courses on sustainability at five technical universities in Europe. This comparison shows a mismatch among the EESD "experts'" and the students' understanding of sustainability, which suggest that sustainability courses in engineering degrees should emphasise the social and institutional aspects versus environmental and technological ones. Moreover, courses should emphasize more the complexity of sustainability. Originality/value: The paper emphasizes the lack of priority that social and institutional aspects are given in sustainability courses and promotes a discussion about how these two elements and complex thinking can increase their importance in the engineering curriculum. (Contains 3 tables and 6 figures.)