The incorporation of sustainability in universities finds the greatest barriers in the field of teaching. The curricula do not usually cover all dimensions of sustainability as most of the experiences are isolated and they do not reach all students. Within a larger study, an exploratory investigation has been carried out on how sustainability competences are being integrated into the programs of both Informatics Engineering and Industrial Engineering degrees of 25 Spanish universities. The main findings suggest that existing courses in the domain of the humanities and engineering projects, as well as the final degree project, are very appropriate areas for developing a holistic and reflective approach. Likewise, there is a lack of environmental issues in Informatics Engineering, and ethical issues do not usually appear in Industrial Engineering courses. In general, there is no systematic and strategic integration along the degree programs. However, inspiring practices have been identified to propose lines of action and a curriculum model to embed sustainability into engineering education coherently and effectively. In addition, some reflections on drivers, opportunities, and challenges to achieve it are presented.