Memristors, namely hysteretic devices capable of changing their resistance in response to applied electrical stimuli, may provide new opportunities for future memory and computation, thanks to their scalable size, low switching energy and nonvolatile nature. We have developed a functionally complete set of logic functions including NOR, NAND and NOT gates, each utilizing a single phase‐change memristor (PCM) where resistance switching is due to the phase transformation of an active chalcogenide material. The logic operations are enabled by the high functionality of nanoscale phase change, featuring voltage comparison, additive crystallization and pulse‐induced amorphization. The nonvolatile nature of memristive states provides the basis for developing reconfigurable hybrid logic/memory circuits featuring low‐power and high‐speed switching.