The area of multiphase variable-speed motor drives in general and multiphase induction motor drives in particular has experienced a substantial growth since the beginning of this century. Research has been conducted worldwide and numerous interesting developments have been reported in the literature. An attempt is made to provide a detailed overview of the current state-of-the-art in this area. The elaborated aspects include advantages of multiphase induction machines, modelling of multiphase induction machines, basic vector control and direct torque control schemes and PWM control of multiphase voltage source inverters. The authors also provide a detailed survey of the control strategies for five-phase and asymmetrical six-phase induction motor drives, as well as an overview of the approaches to the design of fault tolerant strategies for post-fault drive operation, and a discussion of multiphase multi-motor drives with single inverter supply. Experimental results, collected from various multiphase induction motor drive laboratory rigs, are also included to facilitate the understanding of the drive operation.