Employability is becoming increasingly central to the mission and functioning of universities, spurred on by national and supranational agencies, and the demands of marketisation. This article provides a response to the normative dimensions of the question, progressing through four stages: first, there is a brief consideration of the meaning and manifestations of employability and the historical conditions underpinning its emergence; second, the question is addressed of whether employability is a desirable societal and individual aim "per se"; third, there is a discussion of the fundamental purpose of the university, drawing on the well-known accounts of Newman and Collini, before--fourth--addressing the principal question of whether and in what way employability might fit within that purpose. It is argued that employability is a valid aim of universities only in so far as it is consistent with the central purpose of the institution to foster human understanding through open-ended enquiry. Further questions are discussed, namely, whether other social institutions are better equipped to promote employability, possible costs for the university, the ethical dimension and differences between public and private institutions.