The prediction of future weather and climate events relies heavily upon the use of mathematical models in which the physical laws governing the atmosphere are projected forward to the desired time. This is made possible by a fortunate characteristic of the real world, decades of scientific work, and modern computing technology. Such predictions would not be possible were it not for the fact that many of the enormous complications of the real world can be ignored in the mathematical model we use to represent it. Were it necessary to fully initialize and predict every turbulent eddy and sound wave in order to make useful predictions, we probably couldnt make any at all. In fact, however, we are able to approximate all but the largest scale motions and the gross character of the ocean and land surfaces in modeling weather and climate. From the early part of the 20th Century, scientists have continued to improve the realism of the models used, and current versions can predict weather to 7-10 days, and some aspects of climate for a year. Future progress is critically dependent on both scientific advances in modeling some of the less well understood aspects of the system and on continued advances in computational capability.