The endurance of autonomous underwater vehicles (AUVs) has long been constrained by limited energy replenishment. Underwater inductive wireless power transfer (UIWPT), with its contactless power transfer capability, offers an innovative solution for efficient underwater charging of AUVs. This paper provides a systematic review of the architecture of UIWPT systems, analyzes key power loss mechanisms and corresponding optimization strategies, and summarizes the latest research progress in magnetic coupler design, compensation circuit topologies, control methods, simultaneous power and data transfer, and seawater-induced eddy current losses. Representative cases of UIWPT system integration on AUV platforms are also reviewed, with particular emphasis on environmental factors such as salinity variation, biofouling, and deep-sea pressure, as well as EMC, which critically constrain engineering applications. Finally, this paper discusses development trends including high-efficiency power transfer, enhanced reliability under extreme environments, and practical deployment challenges, and it presents a forward-looking technical roadmap towards long-term, autonomous, and intelligent underwater wireless power transfer.