A brief history of the progress in weather forecasting over the past 100+ years is presented. Modern forecast methods use the mathematical framework of of the motion of fluids, treating forecasts as an initial value problem; the evolution of the solution techniques, as the model grid resolutions become finer, are described. The influence of chaos theory on weather forecasting, the shift from deterministic to ensemble forecasting, and the substantial computational requirements to maintain current progress both for operational forecasting and climate modelling are discussed.