This paper pertains to a broader biographical-narrative research project which studies barriers and support as identified by students with disabilities at a Spanish University ["Barriers and Support That Disabled Students Identify in the University". Project funded by the Spanish Ministry of Science and Innovation (Dir. Dr Anabel Moriña; Ref. EDU 2010-16264, 2010-2014)]. The present study focuses specifically on barriers and support identified by students with disabilities enrolled in undergraduate programmes in the Social Sciences and Law. The purpose of this paper is to analyse, from the point of view of disabled students (applying the biographic-narrative methodology), which barriers and which support this group encounters in Higher Education. To this end, findings are organised in the following categories: general institutional data; infrastructure, architectural and accessibility-related data; faculty and teaching-related data; data relating to fellow students; and suggestions for improving the university and/or university classrooms. In the Conclusions section, we return to our earlier discussion of key findings which shed some light on how the University helps or hinders learning among participants in the study. From this perspective, taking as a reference the social model of disability, we conclude that in order to be inclusive, the University needs to commit itself to adopting proactive measures that eliminate the barriers that do not permit the learning and the full participation of the students in question.