The generation and evolution of surface waves (sea and swell) in the Arctic Ocean are controlled by the wind forcing and the sea ice extent, which is obviously different with the tropical and subtropical oceans. We introduce the recent research progresses of Arctic Ocean surface waves under different ice coverage based on the observations of buoys, moorings and ship-based measurements, as well as the studies based on satellite remote sensing and numerical simulations. The propagation mechanisms of waves in sea ice covered areas are also reviewed. The average significant wave height in the open water of the Arctic Ocean in summer can reach 3 m, and during storms, the significant wave height can reach 5 m in the Beaufort Sea. Except for the Atlantic sector, the wave activity in most area of the Arctic Ocean during summer has increased in the past few decades, and the significant wave height on the Beaufort-Chukchi Sea has an increasing trend of about 1-3 cm/a. This trend is mainly caused by the collective effect of increase in fetch due to the sea ice retreat, and frequency and intensity of storms. The projection based on the CMIP5 multi-model simulations shows that compared with the historical period (1979-2005), the significant wave height over the Arctic Ocean at the end of this century (2081-2100) will increase by 3 cm/a, of which the largest increase occurs in the eastern part of the central Arctic Ocean. Increased wave activity promotes the ablation of sea ice through the wave-ice positive feedback mechanism during the melting period. In coastal areas, increased wave activity will accelerate coastal erosion and promote the disintegration of coastal permafrost. Extreme waves can also pose a threat to shipping safety. Future research needs to be conducted based on more and extensive field observations to deepen the understanding of the generation, development, propagation, and attenuation mechanisms of waves under the influence of changes in sea ice extent and thickness, so as to improve the ability to simulate and project waves in ice areas.