The social dimension of higher education seems to have been highlighted in the most recent documents of the European Higher Education Area. Furthermore, the interest in providing future graduates with the competences necessary for their future jobs seems to have grown in recent decades. In this context, the key questions are what social competences could help graduates to enter the world of work and how universities can facilitate the development of such competences. In the present article, we clarify the role of civic and social competence in university education and offer some guidelines to orientate their learning. To address these objectives, the present study is divided into five parts. First, we define what we understand as civic or citizen competence. In the second part, we describe the reasons why we consider that the learning of civic competence may occur in different settings (formal, informal, or non-formal) of university life. We propose character education and integrated learning (IL) as promising approaches to foster civic learning in the third and fourth sections. Finally, we offer recommendations on how university leaders and professors might promote civic or citizenship competence.