  In this paper, we develop sparse grid discontinuous Galerkin (DG) schemes for
the Vlasov-Maxwell (VM) equations. The VM system is a fundamental kinetic model
in plasma physics, and its numerical computations are quite demanding, due to
its intrinsic high-dimensionality and the need to retain many properties of the
physical solutions. To break the curse of dimensionality, we consider the
sparse grid DG methods that were recently developed in
\cite{guo2016sparse,guo2017adaptive} for transport equations. Such methods are
based on multiwavelets on tensorized nested grids and can significantly reduce
the numbers of degrees of freedom. We formulate two versions of the schemes:
sparse grid DG and adaptive sparse grid DG methods for the VM system. Their key
properties and implementation details are discussed. Accuracy and robustness
are demonstrated by numerical tests, with emphasis on comparison of the
performance of the two methods, as well as with their full grid counterparts.
