Autonomous vehicles (AVs) aim to improve safety and comfort of road users while contributing to the reduction of traffic congestion, air pollution, fuel consumption, and enabling mobility and accessibility of disabled and older people. As AV technology is rapidly advancing, there is an urgent need to explore how those new mobility services will impact urban transport systems, including the users, the infrastructure, and the design of future urban areas. This paper applies a systematic review to assess the role of AVs in urban areas. It reviews 41 articles published between 2003 and 2023, and uses inductive and deductive coding approaches to identify seven themes and thirty sub-themes within the literature. The seven include: benefits, attitudes, and behaviours and user perception, climate adaptation, climate mitigation, legislation and regulations, sustainability, and infrastructure. Studies related to benefits accounted for 25% of the sample, followed by behaviours and user perception (24%) and sustainability (22%). The least amount of research has been undertaken on the role of AVs to support climate adaptation. Geographically, almost half (#22) of the papers originate within Europe, followed by America (#10) and Asia (#7). There is only limited research originating from the Global South. This systematic review sets the scene for considering how AVs in public transport can be implemented in urban areas by establishing the current state of knowledge on user attitudes, perceptions, and behaviour, the benefits of AVs, the infrastructure and legislation and regulations required for AVs, and the role AVs have in climate mitigation, adaptation, and sustainability.