Within the university sector, student recruitment and enrolment are key strategies as institutions strive to attract, retain and engage students. This strategy is underpinned by the provision of services, applications and technologies that facilitate lecturing and support staff. Universities that offer online learning have a particular incentive to use modern electronic channels such as chatbots to combine high levels of service and availability. This paper details a thorough literature review which investigates recent chatbot implementation developed within a university setting to assist with student queries not related to classroom learning. It initially describes chatbot examples related to student administration activities and teaching and learning, before describing in detail the recent evolution of Natural Language Processing and the more immediate arrival of state-of-the-art generative techniques. The use of chatbot development platforms is also considered and eight university chatbot implementations are compared and considered in detail. Two of the main findings of the review are that datasets associated with closed domains are still difficult to obtain and curate, and that universities unlike other sectors, have not yet realised the potential for chatbot implementation. Finally, the review suggests approaches that take advantage of already existing data and newer generative models and frameworks that can help in the development of student focused chatbots.