Research on University Mathematics Education is expanding world wide. This chapter aims to provide a synthesis of results, methods and open questions, focusing specifically on the work accomplished in this area during the first 9 European Congresses on Research in Mathematics Education. The chapter does so in four sections. The first gives a short introduction to the subject and its history in the European and international context. The second presents a selection of studies of university mathematics education as it is currently practiced in universities, with a particular focus on the contents and meaning of mathematics at this level, the methods and resources employed in teaching, the more or less evident transition problems related to mathematics education at university, students’ experience and perspectives on mathematics at university, and the functions and relations of mathematics courses in non-mathematics study programmes. The third section surveys intervention oriented research, to experiment innovative methods in the teaching of specific modules, or to support university teachers’ professional development. On this background of rapidly expanding knowledge in the field, the fourth section looks ahead, pointing out potentials and needs for further research, as well as for stronger contributions to and impact on the practice field.