Algebraic based multigrid methods offer a flexible medium for adapting to a wide range of problems, yet traditional approaches have designed the multigrid components for basic, isotropic, and well-behaved phenomena. As a result, out-of-the-box multilevel preconditioners do not handle a wide range of problems. Moreover, the standard components of the multigrid hierarchy are also not directly suited for data parallel computing (e.g. on a GPU or other high-throughput computing unit). In this talk, we highlight some recent advances in generalizing multigrid, and detail an approach to exposing fine-grained parallelism in the multigrid hierarchy.