Numerical weather prediction has provided routine forecasts of global weather for more than thirty years. During the period numerical models have evolved from the use of low resolution balance equations to high resolution fluid dynamics equations with added terms to describe physical processes such as radiative heating and latent heat release. Both grid-point and spectral transform methods have been used. Forecasts require an initial state, and much effort has gone into data assimilation and initialization consistent with the nonlinear dynamics of the models. The chaotic atmosphere is of limited predictability, and deterministic forecasts are only good for about a week. The climate is defined by the statistical properties of the weather, and these change far more slowly. There is much current interest in the response of climate to human influences. Global climate change studies are largely based on weather models of lower resolution that are run for much longer times and averaged. But the search continues for a true climate model that deals directly with slowly evolving statistics.