The 2020 EUA Learning & Teaching Thematic Peer Group on "Meeting skills and employability demands" explored how universities can ensure that their study programmes reflect the dynamic demands of society and the labour market, and address skills demands throughout the student experience. In this paper, employability is considered as part of universities' mission to educate and to contribute in general to future graduates' personal and professional development, including in lifelong learning. It outlines challenges associated with this mission and provides recommendations to tackle them.