Unmanned underwater vehicles (UUVs) have become increasingly popular in recent years due to their use in various applications. The motivations for using UUVs include the exploration of difficult and dangerous underwater environments, military tasks in mine detection, intelligence gathering and surveillance, the inspection of offshore oil and gas infrastructure in the oil and gas industry, scientific research for studying marine life, and the search and rescue of missing persons or submerged airplanes or boats in underwater environments. UUVs offer many advantages in achieving the desired applications with increased safety, efficiency, and cost-effectiveness. However, there are also several challenges associated with their communication, navigation, power requirements, maintenance, and payload limitations. These types of vehicles are also prone to various disturbances caused by currents of the ocean, propulsion systems, and unmolded uncertainties. Practically, it is a challenging task to design a controller that will ensure optimal performance under these conditions. Therefore, the control system design is of prime importance in the overall development of UUVs. Also, the UUV controller receives input from different sensors, and the data from these sensors are used by the controller to perform different tasks. The control systems of UUVs should take into account all uncertainties and make them stable so that all sensors can perform optimally. This paper presents a complete review of different control system design algorithms for UUVs. The basic logic designs of several control system algorithms are also presented. A comparison is made based on reliability, robustness, precession, and the ability of the controller to handle the nonlinearity that is faced by UUVs during their missions. Simulation and experimental results are thoroughly studied to gain insight into each algorithm. The advantages and disadvantages of each algorithm are also presented, which will facilitate the selection of a suitable algorithm for the control system design of UUVs.