The dense Z-pinch project at Imperial College is aimed at achieving radiative collapse to high density in a hydrogen plasma, and also to study plasmas close to controlled fusion conditions. To this end, the MAGPIE generator (2.4 MV, 1.25, and 200 ns) has been built and tested, and is now giving preliminary experimental data at 60% of full voltage for carbon and CD2 fibers. These discharges are characterized by an initial radial expansion followed by the occurrence of m = 0 structures with transient X-ray emission from bright spots. Late in the discharge a disruption can occur, accompanied by hard X-ray emission from the anode due to an energetic electron beam and, in the case of CD2 fibers, a neutron burst. Concomitant theoretical studies have solved the linear stability problem for a Z-pinch with large ion Larmor radii, showing that a reduction in growth rate of m = 0 and m = 1 modes to about 20% of the magnetohydrodynamic (MHD) value can occur for a parabolic density profile when the Larmor radius is optimally 20% of the pinch radius. Two dimensional MHD simulations of Z-pinches in two extremes of focussed short-pulse laserplasma interactions and of galactic jets reveal a nonlinear stabilizing effect in the presence of sheared flow. One-dimensional simulations show that at low line density the lower hybrid drift instability can lead to coronal radial expansion of a Z-pinch plasma.