Abstract: Vortex-induced vibration (VIV) of cylindrical structures is a very common phenomenon in daily life. Cylinder structures, such as pipelines in ocean engineering, high-rise buildings, stay cables in civil engineering and heat exchangers in nuclear engineering, etc. are frequently affected by vortex-induced vibrations, which can induce fatigue damage and make the failure of structures. At present, the VIV mechanism of cylindrical structures in vertical incoming flow has been comprehensively understood. However, when the cylinder structure is inclined in the flow field, the wake flow of the inclined cylinder is significantly different from that of the vertical one, and the fluid-structure interaction mechanism is more complex. Earlier, independence principle (IP) was proposed to simplify the problem of flow around an inclined stationary cylinder. In the assumption of the Independence Principle, the incoming flow velocity can be decomposed into one part that is vertical to the cylinder axis, and the other that is parallel to the cylinder axis. Only the velocity component vertical to the cylinder axis is considered and the influence of the velocity component parallel to the cylinder axis is ignored. In recent years, a large number of experimental and numerical studies have been carried out to investigate the VIV characteristics of an inclined cylinder and the applicability of Independence Principle. To deepen the understanding of the VIV characteristics and mechanisms of inclined cylinder, this paper summarizes and expounds the response characteristic, wake flow characteristic and hydrodynamic characteristic in “vortex-induced vibration of an inclined cylinder.”. The scope of the application of Independence Principle, the VIV mechanisms and VIV suppression of inclined cylindrical structures are discussed in depth, and the future research direction of this problem is prospected.