Underwater applications are rapidly increasing as we explore underwater and marine environments due to their unique characteristics. Due to uncertainties, disturbances, dynamic characteristics, and constraints, the effective design of AUV Subsystem tuning, motion, and PID control systems is always a challenging task. The designed AUV model and its controller need to be robust by adapting to the reference model to overcome the issues that arise in underwater environments. This article presents a detailed view and comprehensive comparison of recently published AUV control methods, strategies, and models. This article also offers a detailed explanation of the mathematical modeling related to the dynamics of AUVs, grounded in the system’s framework. This review also discusses the open problems in AUV tuning and control systems while suggesting the design and development of more novel and innovative strategies for researchers.