Marine heatwaves (MHWs) are prolonged extreme oceanic warm water events. They can have devastating impacts on marine ecosystems — for example, causing mass coral bleaching and substantial declines in kelp forests and seagrass meadows — with implications for the provision of ecological goods and services. Effective adaptation and mitigation efforts by marine managers can benefit from improved MHW predictions, which at present are inadequate. In this Perspective, we explore MHW predictability on short-term, interannual to decadal, and centennial timescales, focusing on the physical processes that offer prediction. While there may be potential predictability of MHWs days to years in advance, accuracy will vary dramatically depending on the regions and drivers. Skilful MHW prediction has the potential to provide critical information and guidance for marine conservation, fisheries and aquaculture management. However, to develop effective prediction systems, better understanding is needed of the physical drivers, subsurface MHWs, and predictability limits.