This paper argues that universities do have responsibilities to their wider communities, and that those responsibilities--or that "engagement"--should be managed in a way that is not solely dictated by the university. The paper, which focuses on UK universities, first explains why the contemporary context makes it important to consider communities in the plural rather than think of a single community. Following this, a range of engagement frameworks are examined in order to consider how a university's responsibilities could be analysed. The existence of multiple frameworks demonstrates that engagement has different purposes and timescales, aspects of which can be illustrated in various ways. The approach of using a framework also allows recommendations to be made for how engagement can be managed, if indeed it can or should be. A framework developed in a report for the National Co-ordinating Centre for Public Engagement is selected as it offers the closest fit for a framework that enables a focus on universities' responsibilities to their wider communities. Case studies are given to highlight some of the issues a university may need to consider when undertaking engagement activity. The paper then investigates what motivates a university to engage and concludes that in seeking to manage the complexity that is engagement in the twenty-first century, a university is also demarcating its aims, purposes and priorities. (Contains 1 table, 2 figures and 1 note.)