The demand on universities to demonstrate their impact (economic, societal, etc.) has come to the forefront of higher education, research and innovation policy. In this paper LERU analyses this trend against recent societal changes, how and why the concept of universities’ impact has changed and the consequences for university research and teaching. LERU advocates a view which sees societal impact as the outcome of the creative encounters of various stakeholders and their contributions to a common goal. In contrast to a traditional view of a uniform, linear knowledge production system, focused on quick economic benefit and easily quantifiable output, our vision of societal impact is seen as the result of a dynamic, open and networked process of productive interactions in a culture of sustained engagement with varying stakeholders. Among the recommendations formulated in the paper is for universities to engage across a broad spectrum with governments, funders, the private sector, civil society and society at large on this basis, and for governments and funders to support and incentivise universities in their endeavours to embrace a broad impact agenda.