In past decades, there has been a growing interest in the discussion and study of using underwater acoustic channel as the physical layer for communication systems, ranging from point-to-point communications to underwater multicarrier modulation networks. A series of review papers were already available to provide a history of the development of the field until the end of the last decade. In this paper, we attempt to provide an overview of the key developments, both theoretical and applied, in the particular topics regarding multicarrier communication for underwater acoustic communication such as the channel and Doppler shift estimation, video and image transmission throw multicarrier techniques, etc. This paper also includes acoustic propagation properties in seawater and underwater acoustic channel representation.