A hysteresis motor produces output torque through the hysteresis effect of magnetic materials. It has the advantages of a simple structure, high-speed operation, high temperature resistance, low noise and self-starting capability. It can be applied to some special occasions requiring high speed and high stationarity. However, its disadvantage is low torque density, low efficiency and low power factor. The permanent magnet hysteresis motor is a compromise of the characteristics of permanent magnet motor and hysteresis motor, and it can be self-starting in the case of having a torque density comparable to that of a permanent magnet motor. In addition, there are some new structures of hysteresis motors, which open up the direction for innovative applications. Due to the complexity of magnetic properties, the calculation methods and dynamic models of hysteresis motors and permanent magnet hysteresis motors are special and also depend on the research of hysteresis materials and hysteresis models. This paper starts from the principle and classification of the hysteresis motor, and different structures and the corresponding analysis methods are reviewed. The motors with new structures and new methods are emphasized, the innovation and contribution of existing research are summarized, and the development trend of hysteresis motors is described.