Cable-stayed bridges serve as backbones in infrastructure networks for its aesthetics and structural advantages against suspension bridges. The interconnections between the deck, the cables, the towers, and their base are complicated in these infrastructures. Natural disasters such as earthquakes caused structural damage and economic losses, prompting international concern about structural safety and the development of different techniques to improve the dynamic performance of cable-stayed bridges. The study provides an overview of several control strategies used in recent research on the seismic response of cable-stayed bridges and discusses about its performances. For seismic response management of bridges, comparative performance research of several seismic control devices such as active, passive, semi-active, and hybrid is carried out. Parametric research is also carried out to investigate the efficacy by varying critical damper parameters. The assessment criteria of the cable-stayed bridge (CSB) issue are discovered by varying the different damper settings. Also, direct comparison of the control strategies is performed based on the evaluation parameter (base shear, overturning moment, deck displacement, etc.) of the benchmark cable strayed bridge.