This book presents a collection of articles written by mathematicians and physicists, designed to describe the state of the art in climate models with stochastic input. They are based on a selection of lectures given at the interdisciplinary Workshop on Stochastic Climate Models held in Chorin, Germany, from May 31 to June 2, 1999. The emphasis is on reduced models tractable with advanced tools from the area of stochastic processes, stochastic analysis and random dynamical systems. They include popular examples such as box models for the thermohaline ocean circulation and simple models for El Niño. Among the main topics addressed are a comprehensive survey of the hierarchy of climate models ranging from general circulation models to simple energy balance models; a discussion of the origin of stochasticity in climate modelling by separation of fast and slow scale processes such as weather phenomena or astronomical events; a review of relevant mathematical tools such as stochastic partial differential equations, aspects of stochastic dynamics, large deviations, and averaging techniques; several concrete reduced models are discussed together with methods for their approach such as stochastic resonance, localization of waves, or tracer transport in stochastic flows. The book is aimed at mathematicians, physicists or scientists of any area interested in an overview of the state of the art in reduced climate models. In particular, mathematicians will find a survey of simple models, while physicists will encounter mathematically relevant techniques at work.