In recent decades, wireless power transfer (WPT) has gained significant interest from both academic and industrial experts. It possesses natural electrical isolation between transmitter and receiver components, ensuring a secure charging mechanism in an underwater scenario. This ground-breaking technology has also enabled power transmission in the deep-sea environment. However, the stochastic nature of the ocean highly influences underwater wireless power transmission and transfer efficiency is not up to that of terrestrial WPT systems. Recently, the research fraternity has focused on WPT in the air medium, while underwater wireless power transfer (UWPT) is challenging and yet to be explored. The major concerns are ocean current disturbance, bio-fouling, extreme pressure and temperature, seawater conductivity and attenuation. Thus, it is essential to address these challenges, which cause a substantial energy loss in UWPT. This study presents a comparison between various WPT techniques and highlights the research contributions in UWPT in recent years. Research and engineering challenges, practical considerations, and applications are analyzed in this review. We have also addressed influencing factors such as coil orientation, coil misalignment and seawater effects in order to realize an efficient and flexible UWPT system. In addition, this study proposes multiple-input and multiple-output (MIMO) wireless power transmission, which can significantly improve the endurance of autonomous underwater vehicles (AUVS). This idea can be applied to the design of an underwater wireless power station for self-charging of AUVs.