Magnetorheological damper (MRD) is a kind of smart damper, with working medium using magnetorheological fluid. At present, it is widely used to reduce the vibration in the fields of buildings, bridges, vehicles and trains, and so on. The working principle of the MRD was introduced. The structures of the MRD, such as, the different excitation coils, the different resistance gaps and the different types of actuators were analyzed in detail. At the same time, the MRD with functional integration of the self-sensing and self-powered ability in displacement test and energy storage were also investigated further. The differential self-induced MRD of design was also expounded. The relevant analysis and conclusion can provide some reference for the structural design and functional integration of the MRD.