The National Oceanic and Atmospheric Administration's (NOAA's) National Weather Service (NWS) issues warnings for severe thunderstorms, tornadoes, and flash floods because these phenomena are a threat to life and property. These warnings are presently based upon either visual confirmation of the phenomena or the observational detection of proxy signatures that are largely based upon radar observations. Convective-scale weather warnings are unique in the NWS, having little reliance on direct numerical forecast guidance. Because increasing severe thunderstorm, tornado, and flash-flood warning lead times are a key NOAA strategic mission goal designed to reduce the loss of life, injury, and economic costs of these high-impact weather phenomena, a new warning paradigm is needed in which numerical model forecasts play a larger role in convective-scale warnings. This new paradigm shifts the warning process from warn on detection to warn on forecast, and it has the potential to dramatically increase warning lead times. A warn-on-forecast system is envisioned as a probabilistic convective-scale ensemble analysis and forecast system that assimilates in-storm observations into a high-resolution convection-resolving model ensemble. The building blocks needed for such a system are presently available, and initial research results clearly illustrate the value of radar observations to the production of accurate analyses of convective weather systems and improved forecasts. Although a number of scientific and cultural challenges still need to be overcome, the potential benefits are significant. A probabilistic convective-scale warn-on-forecast system is a vision worth pursuing.