An emerging concern for lake ecosystems is the occurrence of compound extreme events i.e. situations where multiple within-lake extremes occur simultaneously. Of particular concern are the co-occurrence of lake heatwaves (anomalously warm temperatures) and high chlorophyll-a extremes, two important variables that influence the functioning of aquatic ecosystems. Here, using satellite observations, we provide the first assessment of univariate and compound extreme events in lakes worldwide. Our analysis suggests that the intensity of lake heatwaves and high chlorophyll-a extremes differ across lakes and are influenced primarily by the annual range in surface water temperature and chlorophyll-a concentrations. The intensity of lake heatwaves is even greater in smaller lakes and in those that are shallow and experience cooler average temperatures. Our analysis also suggests that, in most of the studied lakes, compound extremes occur more often than would be assumed from the product of their independent probabilities. We anticipate compound extreme events to have more severe impacts on lake ecosystems than those previously reported due to the occurrence of univariate extremes.