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Permanent magnet synchronous motors (PMSMs) are commonly used in the automation industry. With the speedy development of digital system processors, predictive control as a modern control scheme has been applied to improve the dynamic performance and work efficiency of PMSMs. This paper provides an overview of the research status of PMSM-based predictive control strategies. The deficiencies of the three most popular predictive schemes, deadbeat predictive control, finite-control-set model predictive control, and continuous-control-set model predictive control, and existing improvement strategies such as delay compensation schemes, robust control schemes, and multi-vector control schemes, are summarized. Finally, current technological trends are discussed, emphasizing future research directions for predictive control in PMSM drive systems.