Past work has shown that discretizing dynamical systems in a structure-preserving way can improve upon the performance of numerical methods constructed using more traditional approaches.  We aim to show that the Maxwell-Vlasov system of equations, which models plasma dynamics, is amenable to such a structure-preserving approach.  In particular, we will appeal to results obtained for compressible fluids and electromagnetic fields in our treatment of Maxwell-Vlasov, while discussing obstacles unique to that system.