Underwater optics have seen a notable surge of interest in recent years, emerging as a critical medium for conveying information crucial to underwater resource exploration, autonomous underwater vehicle navigation, etc. The intricate dynamics of underwater optical transmission, influenced by factors such as the absorption by the water and scattering by multiple particles, present considerable challenges. One of the most critical issues is that the optical information representation methods fail to take into account the impact of the underwater physical environment. We conducted a comprehensive review and analysis of recent advancements in underwater optical transmission laws and models. We summarized and analyzed relevant research on the effects of underwater particles and turbulence on light and analyzed the polarization effects in various environments. Then, the roles of various types of underwater optical propagation models were analyzed. Although optical models in complex environments are still mostly based on Monte Carlo methods, many underwater optical propagation mechanisms have been revealed and can promote the impacts of optical information expression. We delved into the cutting-edge research findings across three key domains: the enhancement of underwater optical image quality, the 3D reconstruction from monocular images, and the underwater wireless optical communication, examining the pivotal role played by light transmission laws and models in these areas. Drawing upon our extensive experience in underwater optics, including underwater optical sensor development and experiments, we identified and underscored future directions in this field. We advocate for the necessity of further advancements in the comprehension of underwater optical laws and physical models, emphasizing the importance of their expanded application in underwater optical information representations. Deeper exploration into these areas is not only warranted but essential for pushing the boundaries of current underwater optical technologies and unlocking new potential for their application in underwater optical sensor developments, underwater exploration, environmental monitoring, and beyond.