There are many methods one may use to solve partial differential equations numerically. For large scale problems, direct methods are not computationally feasible and therefore iterative methods tend to be the best option. Multigrid methods are a particularly attractive strategy for certain classes of problems. Roughly speaking, in a multigrid approach, a problem is solved on a hierarchy of grids. The purpose of this talk is to discuss the benefits of a multigrid strategy and various ways it may be introduced in optimization. Of particular interest is the so called nonlinear multigrid scheme.