<p>Permanent magnet synchronous motors (PMSMs) have been widely applied in key fields such as new energy vehicle drives, industrial servo systems, and rail transportation due to their high efficiency, high power density, and excellent control performance. In the control of PMSM, model predictive current control (MPCC) has become one of the current mainstream control strategies because it can flexibly handle multiple constraints and respond quickly to dynamic demands. This article will conduct a review of both continuous control set model predictive control (CCS-MPC) and finite control set model predictive control (FCS-MPC) separately. Through the overview of the principles and the derivation of formulas, it briefly describes the differences and operation processes of the two methods. Furthermore, by first clarifying the core principles of the two methods and combining the derivation of the formulas for the PMSM mathematical model and the cost function, the essential differences and complete operation processes of CCS-MPC and FCS-MPC can be clearly explained. Then, summarize the main application forms of the two types of methods, respectively, and analyze their existing shortcomings (such as the high computational complexity of CCS-MPC and the fluctuation of switching frequency in FCS-MPC), and propose targeted improvement directions. Finally, the discussion focused on the integration trend of PMSM control and artificial intelligence (AI), and several promising research directions were highlighted, providing references for further improvement of PMSM control performance.</p>