Intensifying marine heatwaves (MHWs) are pervasive and destructive manifestations of anthropogenic climate change. Over the past two decades, MHWs have driven biological, ecological and socioeconomic change in almost all oceans and seas. In this Review, we assess the impacts of MHWs on marine organisms and the benefits they provide to people, highlight knowledge gaps and consider opportunities to mitigate MHW impacts. Globally, MHWs have become increasingly intense and frequent, and result in mortality or movement of species when acute temperature thresholds are exceeded. Vulnerability and resilience to MHWs vary among species, but these mortality events have been prominent for habitat-forming foundation species such as corals, kelp and seagrass, causing many cascading indirect impacts on ecosystem functioning and biodiversity. Poleward species shifts produce novel and complex species interactions and altered ecosystem functions, which have considerable consequences for people and their livelihoods. Reducing greenhouse gas emissions remains essential and urgent to address impacts long term, but increases in MHW intensities and duration will be unavoidable and prominent for the foreseeable future. As such, closing the current knowledge gaps around MHWs and their impacts on biodiversity, as well as proactive management strategies, are urgently needed to mitigate further damage to ecosystems and people, and to build resilience into the future.