Axial flux permanent magnet synchronous motors (AFPMSMs) have been widely used in wind-power generation, electric vehicles, aircraft, and other renewable-energy applications owing to their high power density, operating efficiency, and integrability. To facilitate comprehensive research on AFPMSM, this article reviews the developments in the research on the design and control optimization of AFPMSMs. First, the basic topologies of AFPMSMs are introduced and classified. Second, the key points of the design optimization of core and coreless AFPMSMs are summarized from the aspects of parameter design, structure design, and material optimization. Third, because efficiency improvement is an issue that needs to be addressed when AFPMSMs are applied to electric or other vehicles, the development status of efficiency-optimization control strategies is reviewed. Moreover, control strategies proposed to suppress torque ripple caused by the small inductance of disc coreless permanent magnet synchronous motors (DCPMSMs) are summarized. An overview of the rotor-synchronization control strategies for disc contra-rotating permanent magnet synchronous motors (CRPMSMs) is presented. Finally, the current difficulties and development trends revealed in this review are discussed.