We discuss the equilibria and confinement of plasma via the Vlasov-Maxwell model. In the first result, we consider the relativistic Vlasov-Maxwell system (RVM) on a general axisymmetric spatial domain with perfect conducting boundary which reflects particles specularly, assuming axisymmetry in the problem. We construct continuous global parametric solution sets for the time-independent RVM. In the second result, we consider specific situations that correspond physically to z-pinch, theta-pinch, and screw-pinch equilibria in plasma physics. By working in a setting of azimuthal and z-directional invariance, we reduce the existence of electrically neutral, magnetically driven, equilibria of the two-species Vlasov-Maxwell (VM) equation to a second-order ODE. This is joint work with J. Holmer.