Axial-flux permanent-magnet (AFPM) motors are a kind of important motor with compact structure, high power density and high torque density. In this review, the progress of AFPM motors and their key technologies are analyzed and described, with emphasis on the topological structures, design and optimization methods and control techniques. Based on these analyses, the main findings of the review are the following: (1) the yokeless and segment armature (YASA)-type motors have great potential for development; (2) the multi-objective optimization design theories can be integrated and applied to optimize the design of AFPM motors; and (3) optimal control and sensorless control have important value in improving system reliability and reducing cost. Finally, highlights and prospects are provided for further advancing AFPM motors.