Vanadium dioxide undergoes a crystallographic phase transformation at 68°C which is accompanied by a large and abrupt change in resistivity. Two devices, a two-terminal threshold switch and a four-terminal thermal relay, based on this effect are investigated theoretically and experimentally with regard to switching applications. The formation of thermal filaments is found to have a strong influence on both the dc characteristics and on the switching properties. One consequence for both devices is that the power required to sustain the "on" condition is significantly less than that required for switching. It is shown that both devices should be capable of submicrosecond switching times at milliwatt power levels.