In the process of offshore oil well development, the riser is a key component connecting the offshore platform to the subsea oil and gas production system. It is subjected to wind, waves, ocean currents and other external loads throughout the year, which inevitably generates vortex induced vibration (VIV), resulting in the failure of the riser. In severe cases, during the development of offshore oil Wells, vortex-induced vibration may lead to oil and natural gas leakage, and the influence of natural gas hydrate as the internal flow of riser is also relatively large. Under random waves, with the increase of riser length-diameter ratio, the vortex-induced vibration of riser becomes more complex, resulting in increased fatigue damage of riser. Therefore, vortex-induced vibration is an important research field in ocean engineering. In this paper, the latest research progress on the vibration of ocean risers under random waves is reviewed. The characteristics of random wave force are described by Morrison equation, the vibration model of riser is analyzed by ANSYS simulation, and the experimental and numerical studies of typical vortex-induced vibration of Marine riser are described to understand the vortex-induced vibration of Marine riser. It provides the expectation and reference for the future research.