Abstract: An inerter is a two-terminal acceleration-dependent mechanical element for structure control systems. The inerter system is an integrated system for the structural vibration control with inerters. A large number of studies and research projects on the inerter systems have been comprehensively reviewed in this paper. The state-of-the-art of inerter systems in the field of structural vibration control system were discussed from the following three aspects:realization of the inerter mechanism; performance of the inerter system and design of the structures with inerter system. Compared with traditional vibration control systems, the inerter system has its advantages including:the inertia of the structure can be adjusted and the tuning can be achieved flexibly; additional physical mass is negligible when the inertia of the structure changes obviously; the efficiency of energy dissipation is enhanced. This review paper is intended to provide theoretical evidence and practical guidance for the design, application and further development of inerter systems.