Historically, differential equations have originated in chemistry, physics, and engineering. More recently they have also arisen in models in medicine, biology, anthropology, and the like. In this chapter we restrict our attention to ordinary differential equations; a discussion of partial differential equations is a much more complicated issue and is given elsewhere in the book. We focus on initial value problems and present some of the more commonly used methods for solving such problems numerically. References are given where these methods have been implemented in quality software that is available on netlib using anonymous ftp.