The fatigue damage caused by flow-induced vibration (FIV) is one of the major concerns for multiple cylindrical structures in many engineering applications. The FIV suppression is of great importance for the security of many cylindrical structures. Many active and passive control methods have been employed for the vibration suppression of an isolated cylinder undergoing vortex-induced vibrations (VIV). The FIV suppression methods are mainly extended to the multiple cylinders from the vibration control of the isolated cylinder. Due to the mutual interference between the multiple cylinders, the FIV mechanism is more complex than the VIV mechanism, which makes a great challenge for the FIV suppression. Some efforts have been devoted to vibration suppression of multiple cylinder systems undergoing FIV over the past two decades. The control methods, such as helical strakes, splitter plates, control rods and flexible sheets, are not always effective, depending on many influence factors, such as the spacing ratio, the arrangement geometrical shape, the flow velocity and the parameters of the vibration control devices. The FIV response, hydrodynamic features and wake patterns of the multiple cylinders equipped with vibration control devices are reviewed and summarized. The FIV suppression efficiency of the vibration control methods are analyzed and compared considering different influence factors. Further research on the FIV suppression of multiple cylinders is suggested to provide insight for the development of FIV control methods and promote engineering applications of FIV control methods.