Abstract Astounding advances in numerical weather prediction have taken place over the last 40 years. Atmospheric models were rather primitive in the early 1960s and were able to yield modest forecasts at best for one day over a very limited domain at only one to three levels in the atmosphere and for only one or two variables. Today reliable forecasts are produced routinely not only over the entire globe, but over many local regions for periods up to 5 days or longer on as many as 80 vertical levels and for a host of variables. This development is based on dramatic improvements in the models used for prediction, including the numerical methods applied to integrate the prediction equations and a better understanding of the dynamics and physics of the system. Most important is the growth of computing power during this era which allowed the models to expand by more than five orders of magnitude, thus significantly reducing errors and increasing the number and range of variables that can be forecast. Concurrently, the processing of data used by models as initial conditions has also benefited from this explosion in computing resources through the development of highly sophisticated and complex methodology to extract the most information from accessible data (both current and archived). In addition, increased communication speeds allow the use of more data for input to the models and for rapid dissemination of forecast products. Numerous regional models have sprung up to provide numerical forecasts of local weather events with a level of detail unheard of in the past, based on the rapid availability of appropriate data and computational resources. New modeling techniques and methods for reducing forecast errors still further are on the horizon and will require a continuation of the present acceleration in computer processing speeds.