Background <p>The magnetorheological damper (MRD) has a decisive role in the field, where the system’s reaction continuously changes at loaded conditions, such as the vehicle’s suspension system, bridges, and rotor-dynamic systems. The MRD has excellent damping control characteristics in which, the magnetorheological fluid (MRF) behaves as a Newtonian fluid that turns from liquid to semi-solid in the existence of activated magnetic field.</p> Purpose <p>Identification of the parameter which affects the MRD’s damping force and tuning of damping force via control techniques, for diminishing the vibration near resonance in dynamic systems.</p> Methodology <p>This study examines the state of the research in the following arrangements. Initially, the effect of MRD design was investigated, in which optimization of the damping force of the dynamic system is studied by geometrical modifications, i.e., varying the annular gap, coil width, number of coils, piston shape and material of the MRD. The consequence of rheological models on the damping force of MRD connected with vibrating structures was reviewed in the second segment. In the last segment, the effectiveness of different types of control techniques on resonance and system stability was reviewed.</p> Conclusions <p>This review paper will assist in grasping the concept of MRF, influencing parameters of the MRD, and control technique for the abatement of structural vibration in the different dynamic systems. From this review, future directions of research scope in the vibration attenuation problems near resonance using MRDs for different dynamic systems and various unbalance conditions have also been delineated.</p>