EDINSOST is a project aimed at tackling the challenges facing society. It is funded by the Spanish R&D+i Program. The objective of the project is to establish a framework to facilitate the training of graduates capable of leading the resolution of challenges in our society through the integration of sustainability training in the Spanish University System. For the training of graduates, it is essential to train teachers beforehand, since most of them do not possess competencies in sustainability. The EDINSOST project involves fifty-five researchers from ten Spanish Universities. It encompasses five engineering degrees and three degrees related to the three dimensions of sustainability, given their great impact on the short-term challenges confronting society. In view of its multiplier and long-term effect, the project also includes the Bachelor and Master’s degrees of five Education degrees, because graduates from these courses will be the future teachers of new generations of citizens. To achieve its objectives, the project has defined a sustainability competency map for thirteen degrees in the fields of education and engineering. On the basis of this map, the most appropriate didactic strategies for sustainability training will be established, the state of the sustainability training requirements in teachers and students will be diagnosed, and finally, proposals will be made for training both groups. In this paper, the objectives of the EDINSOST project are presented, as well as some results of the first objective: the sustainability competency map for engineering degrees. The map is vital for defining the training needs of teachers and students and is easily adaptable to any engineering degree.