Underwater wireless communication (UWC) means the transmission of data using wireless channels through the underwater, i.e. radio frequency waves (RF), acoustic waves and optical waves in an unguided water environment. In this review article we focus on underwater optical wireless communications (UWOCs) using optical waves as transmission medium. UWOCs have a much higher communication frequency and therefore a much higher data rate compared to RF and acoustic counter-parts. Due to this high-speed data transfer advantage, UWOC has been very attractive over the past few years. Many applications have been proposed in UWOC systems for protection of the environment, underwater exploration, emergency alerts and military operations etc. However, underwater channels also suffer from extreme absorption and dispersion. In recent years, a variety of innovative methods of network architecture have been developed to meet these technological challenges, which are different from standard terrestrial, open space optical communications. In this article we give a detailed overview of various research activities on UWOC. © 2020 IEEE.