Stay cables in cable-stayed bridges are subjected to various types of dynamic excitation mechanisms under environmental loads. The excited vibrations can have a large amplitude because of low vibration frequencies and small inherent damping of cables. As cables become longer (the longest cables are around 600 m in cable-stayed bridges with a main span of 1000 m), more modes are vulnerable to wind and rain-wind induced vibrations, posing challenges to vibration mitigation. This paper presents a comprehensive review of recent advances in stay cable vibration mitigation, including theoretical modeling of cable damping system and techniques for enhancing multimode damping. Recent results on cable damping measurements, understanding of cable vibrations, and relevant aerodynamic countermeasures are also recalled. The reflections can provide guidance for cable vibration control design of cable-supported bridges and for the maintenance/upgrade of cable vibration mitigation system of existing bridges.