Projection between finite element grids and bases arise naturally in the formulation of the finite element method. These projections also form the basis of many important post-processing techniques for superconvergence extractions, a posteriori error estimators and multilevel strategies. In this study we consider the interrelation of these projections for both standard and mixed type finite element methods. Representative examples of projection strategies and their use in superconvergence and error post processing are considered together with supporting numerical experiments. The work also includes results from ongoing investigations of divergence-free projections, the use of least squares mixed methods for adaptive refinement and projections for multigrid and hierarchic multilevel finite element schemes.