Damping augmentation of dynamic structures exposed to uncertain excitations is of key interest to aerospace, mechanical and civil engineers. Magnetorheological (MR) fluid is known to exhibit rapid variations in their rheological properties when subjected to varying magnetic field and thus offers superior potential for applications in smart structures requiring high bandwidth. MR sandwich structures can apply distributed control force to yield variations in stiffness and damping properties of the structure, and thus provide enhanced vibration suppression over a broad range of external excitation frequencies. The objective of this monograph is to present the fundamental investigations on the dynamic characteristics of MR fluid sandwich beams, vibration analysis of fully and partially treated MR fluid sandwich beams, design optimization of the partially treated MR sandwich beam in order to identify optimal locations of the MR fluid segments, and optimal closed loop control strategy for attenuation of vibration of the beam due to the external disturbances.