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The plasma flow switch utilizes the nonlinear and nonuniform dynamics of a plasma discharge in vacuum to accumulate magnetic energy in times of several microseconds and then release this energy to a load in times of a few hundred nanoseconds. Experiments have been performed with capacitor banks up to 6 MJ, providing currents in excess of 107 A and peak voltages over 0.5 MV. Theoretical models include simple slug dynamics coupled to lumped-circuit analyses, magnetoacoustic considerations of one- and two-dimensional aspects of the plasma flow, and two-dimensional magnetohydrodynamic code calculations. The present article reviews both experimental and theoretical efforts, discusses the use of the plasma flow switch to drive plasma liner implosions and high-energy ion flows, and indicates directions for plasma flow switch applications to very high current, high-energy inductive pulsed power systems.