  In this paper we consider Runge-Kutta discontinuous Galerkin (RKDG) schemes
for Vlasov-Poisson systems that model collisionless plasmas. One-dimensional
systems are emphasized. The RKDG method, originally devised to solve
conservation laws, is seen to have excellent conservation properties, be
readily designed for arbitrary order of accuracy, and capable of being used
with a positivity-preserving limiter that guarantees positivity of the
distribution functions. The RKDG solver for the Vlasov equation is the main
focus, while the electric field is obtained through the classical
representation by Green's function for the Poisson equation. A rigorous study
of recurrence of the DG methods is presented by Fourier analysis, and the
impact of different polynomial spaces and the positivity-preserving limiters on
the quality of the solutions is ascertained. Several benchmark test problems,
such as Landau damping, two-stream instability and the KEEN (Kinetic
Electrostatic Electron Nonlinear) wave, are given.
