  We survey the main numerical techniques for finite-dimensional nonlinear
optimal control. The chapter is written as a guide to practitioners who wish to
get rapidly acquainted with the main numerical methods used to efficiently
solve an optimal control problem. We consider two classical examples, simple
but significant enough to be enriched and generalized to other settings:
Zermelo and Goddard problems. We provide sample of the codes used to solve them
and make these codes available online. We discuss direct and indirect methods,
Hamilton-Jacobi approach, ending with optimistic planning. The examples
illustrate the pros and cons of each method, and we show how these approaches
can be combined into powerful tools for the numerical solution of optimal
control problems for ordinary differential equations.
