Tsunamis generated by volcanic eruptions have risen to prominence since the December 2018 tsunami generated by the flank collapse of Anak Krakatau during a moderate eruption and then the global tsunami generated by the explosive eruption of the Hunga volcano in the Tongan Archipelago in January 2022. Both events cause fatalities and highlight the lack in tsunami warning systems to detect and warn for tsunamis induced by volcanic mechanisms. Following the Hunga Tonga—Hunga Ha’apai eruption and tsunami, an ad hoc working group on Tsunamis Generated by Volcanoes was formed by the Intergovernmental Oceanographic Commission of UNESCO. Volcanic tsunamis differ from seismic tsunamis in that there are a wide range of source mechanisms that can generate the tsunamis waves and this makes understanding, modelling and monitoring volcanic tsunamis much more difficult than seismic tsunamis. This paper provides a review of both the mechanisms behind volcanic tsunamis and the variety of modelling techniques that can be used to simulate their effects for tsunami hazard assessment and forecasting. It gives an example of a volcanic tsunami risk assessment undertaken for Stromboli, outlines the requirement of volcanic monitoring to warn for tsunami hazard and provides examples of volcanic tsunami warning systems in Italy, the Hawaiian Island (USA), Tonga and Indonesia. The paper finishes by highlighting the need for implementing monitoring and warning systems for volcanic tsunamis for locations with submarine volcanoes or near-shore volcanoes which could potentially generate tsunamis.