Discrete differential forms are a generalization of the common H¹()-conforming Lagrangian elements. For the latter, Galerkin schemes based on sparse grids are well known, and so are fast iterative multilevel solvers for the discrete Galerkin equations. We extend both the sparse grid idea and the design of multilevel methods to arbitrary discrete differential forms. The focus of this presentation will be on issues of efficient implementation and numerical studies of convergence of multigrid solvers.