Underwater acoustic communication is essential in applications like remote control in the offshore oil industry, pollution monitoring in environmental systems, collection of scientific data recorded at ocean-bottom stations, disaster detection and early warning and underwater surveillance. Research on underwater wireless communication techniques plays a vital role in further exploring oceans and other marine environments. There has been an extensive growth in the volume of literature for underwater acoustic (UWA) communication but still it remains to be one of the most challenging areas of wireless communication. Over the years attention has turned on applying modified versions of multicarrier (MC) communication to underwater channel. This paper reviews the recent developments in the area of UWA communication related to multicarrier communication and particularly to orthogonal frequency division multiplexing (OFDM) with respect to applied, theoretical and simulation studies. An attempt has been made to present a compact yet exhaustive literature survey that will serve as a standard reference for researchers working in the area. Stress has been laid on the physical layer issues as it works as the basic foundation of any network. The focus areas of research activities have been identified and a summary of the ongoing activities and future trends has been presented.