Model predictive control (MPC) has been widely applied to ac electric drives over the last decade. Despite the proposed solutions, researchers are still seeking to find more effective solutions for weighting factor (WF) design, parameter dependency, current/torque harmonics, variable switching frequency, and computational complexity. This article presents a comprehensive review of the WF design techniques for finite control set MPC strategies for ac electric drives. First, the article introduces the conventional MPC techniques for electric drives over permanent magnet synchronous motors. Second, WF design methods are discussed under two main headings: WF selection and WF elimination methods. Third, the ongoing challenges and future trends are addressed by considering the current literature. Based on this review, it is obvious that each WF design method still has problems that await more effective solutions. Finally, this article reviews various WF design methods for ac electric drives, reveals the advantages and disadvantages of existing methods in terms of control performance, flexibility, design complexity, and computational complexity, and highlights future trends.