Abstract: Purpose of Review: Review our current understanding of how precipitation is related to its thermodynamic environment, i.e., the water vapor and temperature in the surroundings, and implications for changes in extremes in a warmer climate. Recent Findings: Multiple research threads have i) sought empirical relationships that govern onset of strong convective precipitation, or that might identify how precipitation extremes scale with changes in temperature; ii) examined how such extremes change with water vapor in global and regional climate models under warming scenarios; iii) identified fundamental processes that set the characteristic shapes of precipitation distributions. While water vapor increases tend to be governed by the Clausius-Clapeyron relationship to temperature, precipitation extreme changes are more complex and can increase more rapidly, particularly in the tropics. Progress may be aided by bringing separate research threads together and by casting theory in terms of a full explanation of the precipitation probability distribution.