Hasselmann (1976) has recently proposed a stochastic model of climate variability where climatic changes are caused by the intrinsic variability of the weather fluctuations. The complete atmosphere--ocean--cryosphere-land system is separated into long time scale cl imate components (mainly the ocean and the cryosphere) and short time scale wea ther components (mainly the atmosphere). The weather components exhibit stochastic fluctuations with a dominant t ime scale of a few days, reflecting instabilities of the atmospheric circulation. Because of their much larger time scale, the climate components respond essentially as integrators of the atmospheric forcing, which acts as an internal white noise generator. The random-walk climate fluctuations that develop have a variance which grows linearly with time, until feedback processes become important and lead eventually to a statistically stationary climate state. A red frequency spectrum is predicted for the climate variance, in general agreement with observations over a broad range of time scales, as reviewed below (see also Mitchell, 1976). The general theory is given in Hasselmann (1976). Here we shall introduce the formalism in the simpler context of sea surface temperature anomalies, and present new comparisons of the model predictions with observations in the North Pacific. It is shown that a single model reproduces the principal features and the seasonal variability of the large-scale sea-surface temperature anomalies observed in mid-latitudes. Other applications of the stochastic climate models are then reviewed. Quasi-geostraphic motions in the ocean interior and yearly and zonally averaged world temperature fluctuations induced by the natural variability of the atmosphere are discussed. The magnitude of