Submitted to IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Sevilla 2003.A geometric derivation of numerical integrators for nonholonomic systems and optimal control problems is obtained. It is based in the classical technique of generating functions adapted to the special features of nonholonomic systems and optimal control problems.This work has been supported by grant BFM2001-2272. A. Santamaría Merino wishes to thank the Programa de formación de Investigadores of the Departamento de Educación, Universidades e Investigación of the Basque Government (Spain) for financial support.Peer reviewed