This chapter is devoted to boundary value problems for ordinary differential equations. It begins with analysis of the existence and uniqueness of solutions to these problems, and the effect of perturbations to the problem. The first numerical approach is the shooting method. This is followed by finite differences and collocation. Finite elements allow for the development of very high order methods for many boundary value problems, but their analysis typically requires sophisticated ideas from real analysis. The chapter ends with the application of deferred correction to both collocation and finite elements.