In resistive evolution a quasistatic plasma is assumed to be in mechanical equilibrium at every instant of time. Equilibria are determined, in part, by magnetic flux constraints. The evolution of these flux constraints depends only on the electric field parallel to the magnetic field, as given by Ohm's law. The use of a new, magnetic-vector-potential formalism for the resistive evolution problem is discussed. This formalism has advantages of generality and simplicity as well as providing greater numerical accuracy in certain cases (such as the evolution of a magnetic island) where artificial singularities occur when using magnetic surface variables. Sample calculations of the evolution of a strongly driven (pinch) discharge with cylindrical symmetry and of the nonlinear growth of a helically symmetric m = 2 magnetic island in the Rutherford regime are given.