There is enormous recent interest in the development of models for rate processes because rates are an almost universal characterization in the physical and biological sciences. In this paper we provide an introduction to several of the problems to be discussed in greater depth by other speakers at a symposium held at the National Institutes of Health on May 6-8, 1985. This review will focus on (1) the Smoluchowski model for reaction rates together with its extension by Onsager, (2)first passage time formalism for discrete and continuous master equations and Fokker-Planck equations, (3)the Kramers model and its extensions, (4) diffusion in the presence of trapping centers.