Ever since 1958, when Oscar Anderson observed copious neutrons emanating from a "magnetically self-constricted column of deuterium plasma," scientists have attempted to develop the simple linear pinch into a fusion power source. After all, simple calculations show that if one can pass a current of slightly less than 2 million amperes through a stable D-T plasma, then one could achieve not just thermonuclear break-even, but thermonuclear gain. Moreover, several reactor studies have shown that a simple linear pinch could be the basis for a very attractive fusion system. The problem is, of course, that the seemingly simple act of passing 2 MA through a stable pinch has proven to be quite difficult to accomplish. The pinch tends to disrupt due to instabilities, either by the m=0 (sausage) or m=1(kink) modes. Curtailing the growth of these instabilities has been the primary thrust of z-pinch fusion research, and over the years a wide variety of formation techniques have been tried. The early pinches were driven by relatively slow capacitive discharges and were formed by imploding a plasma column, The advent of fast pulsed power technology brought on a whole new repertoire of formation techniques, including: fast implosions, laser or field-enhanced breakdown in a uniform volume of gas, a discharge inside a small capillary, a frozen deuterium fiber isolated by vacuum, and staged concepts in which one pinch implodes upon another. And although none of these have yet to be successful, some have come tantalizingly close. This paper will review the history of this four-decade long quest for fusion power.