Axial flux switched reluctance (AFSR) motors combine the characteristics of switched reluctance motors and axial flux motors. It has several advantages, including a simple structure, low manufacturing and maintenance costs, short axial length, adjustable air gap, and strong adaptability to harsh environments, such as high temperatures. These advantages make AFSR motors suitable for high-reliability and fault-tolerant applications in industries like aerospace, new energy vehicles, and intelligent manufacturing. In recent years, AFSR motors have attracted growing attention. This paper reviews the latest research in the field of AFSR motors, introducing their basic principles and four key topological structures: single-stator-single-rotor, single-stator-double-rotor, double-stator-single-rotor, and multi-stator-multi-rotor. This paper also discusses advancements in AFSR motor design, focusing on electromagnetic design calculation methods, algorithm acceleration, core materials, manufacturing processes, and optimization of electromagnetic properties. Based on the unique features of AFSR motor topological structures, this paper summarizes current research on loss analysis and suppression, temperature rise and heat dissipation, torque ripple analysis and suppression, and motor fault and structural strength analysis. Furthermore, this paper introduces control systems for AFSR motors and highlights innovations in control strategies developed by researchers worldwide. Finally, it presents applications of AFSR motors in electric vehicles, wind power generation, and industrial equipment, and provides an outlook on future research directions and development trends. The review work in this paper provides valuable references for both theoretical research and practical engineering applications of AFSR motors.