AbstractHeat waves (HWs) can cause large socioeconomic and environmental impacts. The observed increases in their frequency, intensity and duration are projected to continue with global warming. This review synthesizes the state of knowledge and scientific challenges. It discusses different aspects related to the definition, triggering mechanisms, observed changes and future projections of HWs, as well as emerging research lines on subseasonal forecasts and specific types of HWs. We also identify gaps that limit progress and delineate priorities for future research. Overall, the physical drivers of HWs are not well understood, partly due to difficulties in the quantification of their interactions and responses to climate change. Influential factors convey processes at different spatio‐temporal scales, from global warming and the large‐scale atmospheric circulation to regional and local factors in the affected area and upwind regions. Although some thermodynamic processes have been identified, there is a lack of understanding of dynamical aspects, regional forcings and feedbacks, and their future changes. This hampers the attribution of regional trends and individual events, and reduces the ability to provide accurate forecasts and regional projections. Sustained observational networks, models of diverse complexity, narrative‐based methodological approaches and artificial intelligence offer new opportunities toward process‐based understanding and interdisciplinary research.