Underwater wireless communication has gained a great deal of attention in the last couple of decades because of its applications in the military, industrial, and monitoring sectors. Despite the extreme physical and MAC layer difficulties, acoustics are used for various applications among the various modes of underwater communication technologies used. While significant research efforts have been made to address these issues, the bottleneck remains in achieving high bandwidth, high throughputs, and data rate. Researchers have begun to look into full duplex (FD) implementation to improve bandwidth efficiency and increase data rate and throughput. Users can send and receive data simultaneously over the FD links, maximizing bandwidth utilization and increasing throughput. As a result, we thoroughly reviewed various FD physical layered UWAC systems and MAC layered protocols for underwater communication. The various problems that the aforementioned systems and protocols have faced, as well as the solutions suggested in previous works to solve each problem, are also highlighted. Various metrics are used to compare the performance of various physical layered FD systems and FD MAC protocols. We also explore some of the open research questions in these FD-physical layered and MAC layered protocols, as well as future research directions. Based on ample information, we suggest a cross-layered architecture based on various IBFD-SI cancellations, DA-CSMA, and FD-MAC protocols. This review provides a broad view of the current FD physical and MAC layered protocols based on acoustic communication, as well as recommendations.