It sounds straightforward. As the Earth warms due to the increased concentration of greenhouse gases in the atmosphere, global temperatures rise and so heatwaves become warmer as well. This means that a fixed temperature threshold is passed more often: the probability of extreme heat increases. However, land use changes, vegetation change, irrigation, air pollution, and other changes also drive local and regional trends in heatwaves. Sometimes they enhance heatwave intensity, but they can also counteract the effects of climate change, and in some regions, the mechanisms that impact on trends in heatwaves have not yet been fully identified. Climate models simulate heatwaves and the increased intensity and probability of extreme heat reasonably well on large scales. However, changes in annual daily maximum temperatures do not follow global warming over some regions, including the Eastern United States and parts of Asia, reflecting the influence of local drivers as well as natural variability. Also, temperature variability is unrealistic in many models, and can fail standard quality checks. Therefore, reliable attribution and projection of change in heatwaves remain a major scientific challenge in many regions, particularly where the moisture budget is not well simulated, and where land surface changes, changes in short-lived forcers, and soil moisture interactions are important.