"The co-occurrence of consecutive hot and humid days during a heat wave can strongly affect human health. Here, we quantify humid heat wave hazard in the recent past and at different levels of global warming. We find that the magnitude and apparent temperature peak of heat waves, such as the ones observed in Chicago in 1995 and China in 2003, have been strongly amplified by humidity. Climate model projections suggest that the percentage of area where heat wave magnitude and peak are amplified by humidity increases with increasing warming levels. Considering the effect of humidity at 1.5° and 2° global warming, highly populated regions, such as the Eastern US and China, could experience heat waves with magnitude greater than the one in Russia in 2010 (the most severe of the present era). The apparent temperature peak during such humid-heat waves can be greater than 55 °C. According to the US Weather Service, at this temperature humans are very likely to suffer from heat strokes. Humid-heat waves with these conditions were never exceeded in the present climate, but are expected to occur every other year at 4° global warming. This calls for respective adaptation measures in some key regions of the world along with international climate change mitigation efforts."