Permanent magnet eddy current couplers (PMECCs) have the characteristics of contactless torque transmission, removal of torque ripple, smooth dynamic process, and adjustable speed, and can be used as couplings, dampers, brakes, and speed governors. Their applications in industry, vehicles, and energy fields are gradually expanding. At the same time, the requirements for the torque density and dynamic performance of PMECCs are increasing. Therefore, a large amount of research work has focused on the fast and accurate modeling, design, and optimization of PMECCs. This paper provides a survey on the development of PMECCs technology. The main topics include the structure and classification of PMECCs, modeling methods, loss and heat transfer analysis modeling, and optimization design. In addition, this paper shows the future trends of PMECCs research. All the highlighted insights and suggestions of this review will hopefully lead to increasing efforts toward the model’s construction and the optimal design of PMECCs for future applications.