This chapter describes some of the recent studies on the optimal control of structures. Initially, different passive, active and semi-active control devices are introduced and the importance of optimization in each case is discussed. A comprehensive literature review on the optimal design of various well-known control devices of each category i.e., Tuned Mass Damper (Active, Passive and Semi-Active modifications), Fluid Viscous Damper (Passive and Semi-Active), Viscoelastic Damper and Base Isolation (Passive and Semi-Active) and Active Tendon with special attention to the first studies and studies performed in the last decades, is presented. To suppress tall building vibrations subjected to wind and seismic loads, Tuned Mass Dampers (TMDs) modification have recently gained attention due to their simplicity, stability and reliability. Therefore, in the last section, the results of some recent studies on the optimization of Active and passive Tuned Mass Dampers and a recently proposed promising modification of TMD (i.e. Tuned Mass Damper Inerter) are comprehensively discussed.
