An important constraint on our ability to numerically simulate physical processes is our ability to solve the resulting linear systems. Multiscale methods, such as multigrid, provide optimal or near optimal order solution techniques for a wide range of problems. The biggest drawback to current multigrid methods (both geometric and algebraic) is their fragility. Classical geometric multigrid methods are effective only in simple geometries and only for a relatively small class of problems. Algebraic multigrid methods are free from most constraints on geometry, but they are still only effective for a relatively small class of problems. We seek to identify current roadblocks to obtaining optimal multigrid efficiency and use this knowledge to gain insight into the operation of current multigrid methods. We also propose to investigate the construction of more robust multigrid methods.