The growing number of underwater activities is giving momentum to the development of new technologies, such as buoys, remotely operated vehicles, and autonomous underwater vehicles. The data collected by these vehicles need to be transmitted to a high-speed central unit. Clearly, wired solutions are not suitable, since they strongly impact the mobility. In this scenario, a promising solution is offered by underwater optical wireless communication (UOWC) technology, which can achieve both high-speed and wireless operation. Here, we provide a comprehensive survey on the challenges, the experimental realizations, and the state of the art in UOWC researches.