Heavy precipitation, which in many contexts is welcomed because it provides the water necessary for agriculture and human use, in other situations is responsible for deadly and destructive flash flooding. Over the 30-year period from 1986 to 2015, floods were responsible for more fatalities in the United States than any other convective weather hazard (www.nws.noaa.gov/om/hazstats.shtml), and similar findings are true in other regions of the world. Although scientific understanding of the processes responsible for heavy rainfall continues to advance, there are still many challenges associated with predicting where, when, and how much precipitation will occur. Common ingredients are required for heavy rainfall to occur, but there are vastly different ways in which the atmosphere brings the ingredients together in different parts of the world. Heavy precipitation often occurs on very small spatial scales in association with deep convection (thunderstorms), factors that limit the ability of numerical models to represent or predict the location and intensity of rainfall. Furthermore, because flash floods are dependent not only on precipitation but also on the characteristics of the underlying land surface, there are fundamental difficulties in accurately representing these coupled processes. Areas of active current research on heavy rainfall and flash flooding include investigating the storm-scale atmospheric processes that promote extreme precipitation, analyzing the reasons that some rainfall predictions are very accurate while others fail, improving the understanding and prediction of the flooding response to heavy precipitation, and determining how heavy rainfall and floods have changed and may continue to change in a changing climate.