Many of the earliest experiments in controlled thermonuclear fusion research were Z -pinches. However these pinches were found to be highly unstable to the m = 0, the m — 1 (kink), and the Rayleigh-Taylor instability. The addition of an axial magnetic field and the removal of end losses by proceeding to a toroidal geometry has led to the class of discharges known as tokamaks and the reversed field pinch. But, at fusion temperatures and with practical values of applied magnetic field this restricts the plasma density to 10 20 to 10 21 m- 3 , thereby requiring a containment time of several seconds and a plasma radius of about 1 m. Meanwhile studies of the plasma focus, which after its three-dimensional compression closely resembles a Z -pinch, have shown that a plasma of density 10 25 m- 3 and temperature 1 keV can be achieved in a narrow filament of radius 1 mm. It has enhanced stability properties which might be attributable to the effects of finite ion Larmor radius. Its neutron yield in deuterium can be as high as 10 12 per discharge, with a favourable empirical scaling law, but the thermonuclear origin of the neutrons is doubtful because of the evidence of centre-of-mass motion and the formation of electron and ion beams. The development of high voltage, high current pulse technology has permitted the reconsideration of the Z -pinch to attain dense fusion plasmas which might be stabilized by scaling the ion Larmor radius to be comparable with the pinch radius. Experiments at Imperial College show that the plasma remains stationary for about twenty Alfven radial transit times, limited only by the period of the current waveform. Theory indicates that a dense compact Z -pinch can satisfy Lawson conditions with a power input dependent on the enhanced stability time, or, if stable, with ohmic heating balancing axial heat losses. Preliminary results on a laser-initiated Z -pinch are also presented.