This paper describes the NOAA tsunami forecast software, which incorporates real-time measurements of sea level from DART® tsunami detection buoys into computer models to provide accurate tsunami forecasts. The tsunami forecast software is deployed at the U.S. Pacific and West Coast- Alaska Tsunami Warning Centers. Forecast products include estimates of tsunami amplitudes, flow velocities and arrival times for offshore, coastal and inundation areas. Real-time tsunami predictions for selected coastal locations are provided by forecast inundation models, while the tsunami is propagating through the open ocean, before the waves have reached many coastlines. New research forecast products indicate how the present forecast warnings can be expanded to provide more detailed information about currents and flooding and in harbors.