This paper is intended not as a survey, but as an introduction to some ideas behind the class of mesh adaptive direct search (MADS) methods. Space limitations dictate a brief description of various key topics be provided along with several references, which themselves provide further references. The convergence theory for the methods presented here make a case for closing the gap between nonlinear optimizers and nonsmooth analysts. However these methods are certainly not of purely theoretical interest; they are successful on difficult practical problems. To encourage further use, we give references to available implementations. MADS is implemented in the direct search portion of the MathWorks MATLAB Genetic Algorithm and Direct Search (GADS) Toolbox.