The ZT-40 reversed-field pinch (RFP) has been operated in several modes: (1) without reversed toroidal field, (2) with self reversal, and (3) with aided reversal. An analytic ohmic heating and ignition model both confirm and provide guidance for transport codes. Nondissipative formation schemes have been analyzed and ideal MHD stable evolution and burn scenarios have been found. Particle and fluid simulations have produced qualitative agreement with respect to the nonlinear behavior of m = 0 resistive g-modes. Helical ohmic reversed field states are produced by a 2-D dynamical simulation, and nonlinear analytic work describes the final state. A fast resistive MHD code for linear stability has clarified the relations between several kinds of resistive instabilities. Ballooning modes and g-modes in systems with arbitrary magnetic shear including resistivity and viscosity, have been studied in a unified treatment with growth rate vs wavenumber showing the existence of important cutoffs