Recent research on the projection of precipitation extremes has either focused on conceptual physical mechanisms that generate heavy precipitation or rigorous statistical methods that extrapolate tail behavior. However, informing both climate prediction and impact assessment requires concurrent physically and statistically oriented analysis. A combined examination of climate model simulations and observation-based reanalysis data sets suggests more intense and frequent precipitation extremes under 21st-century warming scenarios. Utilization of statistical extreme value theory and resampling-based uncertainty quantification combined with consideration of the Clausius-Clapeyron relationship reveals consistently intensifying trends for precipitation extremes at a global-average scale. However, regional and decadal analyses reveal specific discrepancies in the physical mechanisms governing precipitation extremes, as well as their statistical trends, especially in the tropics. The intensifying trend of precipitation extremes has quantifiable impacts on intensity-duration-frequency curves, which in turn have direct implications for hydraulic engineering design and water-resources management. The larger uncertainties at regional and decadal scales suggest the need for caution during regional-scale adaptation or preparedness decisions. Future research needs to explore the possibility of uncertainty reduction through higher resolution global climate models, statistical or dynamical downscaling, as well as improved understanding of precipitation extremes processes.