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Model predictive control (MPC) technology for multi-phase electric drives has received increasing attention in modern industries, especially in electric vehicles, marine electrical propulsion, and wind power generation. However, MPC has several challenges in controlling multi-phase electric drives, including the design of weighting factors, high computational complexity, large harmonic currents, heavy reliance on the system model, fault-tolerant control operation, common-mode voltage, and zero-sequence current hazards. Therefore, this paper gives a comprehensive review of the latest and most effective solutions to the existing major technical challenges and prospects for the future trends of MPC for multi-phase electric drives.