Internet of underwater things (IoUT) attracts many interests in these years both in academia and industry, such as marine data collection, pollution monitoring, and offshore exploration. As a fundamental issue of IoUT, the underwater acoustic channel experiences long delay and temporal-spatial uncertainty compared with terrestrial communications and networks. It is difficult to capture full characteristics of the underwater acoustic channel by statistical models. In this paper, we investigate the properties of acoustic propagation in seawater and different underwater acoustic channel models. Moreover, we survey five underwater acoustic channel models, including ray-theoretical model, normal mode model, multipath expansion model, fast-field model, and parabolic equation model, which are the corresponding solutions of the wave equation. We conclude the paper with the characteristics of each model in terms of different aspects.