Global warming is expected to lead to a large increase in atmospheric water vapor content and to changes in the hydrological cycle, which include an intensification of precipitation extremes. The intensity of precipitation extremes is widely held to increase proportionately to the increase in atmospheric water vapor content. Here, we show that this is not the case in 21st-century climate change scenarios simulated with climate models. In the tropics, precipitation extremes are not simulated reliably and do not change consistently among climate models; in the extratropics, they consistently increase more slowly than atmospheric water vapor content. We give a physical basis for how precipitation extremes change with climate and show that their changes depend on changes in the moist-adiabatic temperature lapse rate, in the upward velocity, and in the temperature when precipitation extremes occur. For the tropics, the theory suggests that improving the simulation of upward velocities in climate models is essential for improving predictions of precipitation extremes; for the extratropics, agreement with theory and the consistency among climate models increase confidence in the robustness of predictions of precipitation extremes under climate change.global warming ͉ hydrological cycle ͉ rainfall ͉ extreme events I n simulations of 21st century climate change scenarios, mean precipitation generally increases in the deep tropics and extratropics and decreases in the subtropics (1-3). However, precipitation extremes (defined, for example, as a high percentile of daily precipitation) increase almost across the globe (2, 3), with expected societal impacts such as increased flooding and soil erosion (4). Precipitation extremes are widely held to increase proportionately to the mean atmospheric water vapor content (5, 6), or to the amount of water vapor converging at the base of storms (7). Global-mean water vapor content increases strongly in global warming simulations, at a rate of ϳ7.5% K Ϫ1 with respect to surface temperature, approximately consistent with a constant effective relative humidity (1). Precipitation extremes are thought to increase at a similar rate, or maybe even more rapidly if the strength of the updrafts associated with extreme precipitation events increases as the climate warms (5, 6).However, although precipitation extremes in simulations increase as the climate warms, their rate of increase varies with latitude and is generally not equal to the rate of increase in atmospheric water vapor content (6). Simulations of a wide range of climates with an idealized general circulation model show that precipitation extremes outside the subtropics scale more similarly to mean precipitation than to water vapor content (8). In simulations with comprehensive climate models, the rate of increase in precipitation extremes varies widely among models, particularly in the tropics (2). The variations among models in the tropics indicate that simulated precipitation extremes may depend sensitively on the parameterizatio...