Purpose Structural vibration is principally caused by ground motion excitation. Its control strategy has attracted and still attracts considerable attention. Over the past few years, structural safety was the main objective in the development of construction technics. Methods Recently, most researches focused on the development of these strategies to propose an adequate choice that ensures the safety of structures subjected to the dynamic excitation. The oldest control strategy in the literature is the passive one, in which the reduction of structural vibration caused by ground motion excitation is assured without the need for a source of energy. Results In this paper, an overview, assessment, and state of the art of control strategies especially the passive ones, is presented covering their theoretical backgrounds. The chronological development of these strategies is also provided and analyzed. Conclusion Finally, the last researches, technics and applications in this area are presented and discussed.