The vibration mechanism of the stay cables of long span cable-stayed bridges is complex, the hazards of the vibration are severe and therefore, the additional damping techniques need to be applied to suppress the vibration. In this paper, the researches of the vibration characteristics of the stay cables and vibration suppression mechanism of the dampers applicable to the stay cables are summarized. The Scruton numbers of the longest stay cables of 34 cable-stayed bridges are firstly collected and calculated. The calculations of the Scruton numbers are analyzed and compared to the existing theoretic analysis and wind tunnel test results, are verified by the conclusions from the implemented projects and the target damping parameters for the vibration suppression corresponding to each potential vortex-induced vibration, rain vibration, parameter resonance, internal resonance and wake galloping are determined. Then the damping action mechanism, displacement transfer types and durability of the common dampers are respectively analyzed and compared and the applicable ranges of the different dampers are put forward. Finally, in the two aspects of the action mechanism and test verification, the advantages of the damping efficiency of the lever mass damper (LMD) are particularly introduced and the further research fields of the damping techniques for the stay cables are pointed out. ©, 2015, Wuhan Bridge Research Institute. All right reserved.