Managing COVID−19 within a university setting presents unique challenges. At the start of term, students arrive from geographically diverse locations and potentially have higher numbers of social contacts than the general population, particularly if living in university halls of residence accommodation. Mathematical models are useful tools for understanding the potential spread of infection and are being actively used to inform policy about the management of COVID−19. Our aim was to provide a rapid review and appraisal of the literature on mathematical models investigating COVID−19 infection in a university setting. We searched PubMed, Web of Science, bioRxiv/ medRxiv and sought expert input via social media to identify relevant papers. BioRxiv/ medRxiv and PubMed/Web of Science searches took place on 3 and 6 July 2020, respectively. Papers were restricted to English language. Screening of peer−reviewed and pre−print papers and contact with experts yielded five relevant papers − all of which were pre−prints. All models suggest a significant potential for transmission of COVID−19 in universities. Testing of symptomatic persons and screening of the university community regardless of symptoms, combined with isolation of infected individuals and effective contact tracing were critical for infection control in the absence of other mitigation interventions. When other mitigation interventions were considered (such as moving teaching online, social/physical distancing, and the use of face coverings) the additional value of screening for infection control was limited. Multiple interventions will be needed to control infection spread within the university setting and the interaction with the wider community is an important consideration. Isolation of identified cases and quarantine of contacts is likely to lead to large numbers of students requiring educational, psychological and behavioural support and will likely have a large impact on the attendance of students (and staff), necessitating online options for teaching, even where in−person classes are taking place. Models were highly sensitive to assumptions in the parameters, including the number and type of individuals contacts, number of contacts traced, frequency of screening and delays in testing. Future models could aid policy decisions by considering the incremental benefit of multiple interventions and using empirical data on mixing within the university community and with the wider community where available. Universities will need to be able to adapt quickly to the evolving situation locally to support the health and wellbeing of the university and wider communities.