Lake ecosystems, and the organisms that live within them, are vulnerable to temperature change(1-5), including the increased occurrence of thermal extremes(6). However, very little is known about lake heatwaves-periods of extreme warm lake surface water temperature-and how they may change under global warming. Here we use satellite observations and a numerical model to investigate changes in lake heatwaves for hundreds of lakes worldwide from 1901 to 2099. We show that lake heatwaves will become hotter and longer by the end of the twenty-first century. For the high-greenhouse-gas-emission scenario (Representative Concentration Pathway (RCP) 8.5), the average intensity of lake heatwaves, defined relative to the historical period (1970 to 1999), will increase from 3.7 +/- 0.1 to 5.4 +/- 0.8 degrees Celsius and their average duration will increase dramatically from 7.7 +/- 0.4 to 95.5 +/- 35.3 days. In the low-greenhouse-gas-emission RCP 2.6 scenario, heatwave intensity and duration will increase to 4.0 +/- 0.2 degrees Celsius and 27.0 +/- 7.6 days, respectively. Surface heatwaves are longer-lasting but less intense in deeper lakes (up to 60 metres deep) than in shallower lakes during both historic and future periods. As lakes warm during the twenty-first century(7,8), their heatwaves will begin to extend across multiple seasons, with some lakes reaching a permanent heatwave state. Lake heatwaves are likely to exacerbate the adverse effects of long-term warming in lakes and exert widespread influence on their physical structure and chemical properties. Lake heatwaves could alter species composition by pushing aquatic species and ecosystems to the limits of their resilience. This in turn could threaten lake biodiversity(9) and the key ecological and economic benefits that lakes provide to society.