Air-entraining vortices at hydraulic intakes pose significant challenges to the safe operation of pumped storage hydropower plants (PSH). These vortices can induce structural vibrations, reduce discharge capacity, and damage equipment. This paper comprehensively reviews the current research progress on the formation mechanisms, hydraulic characteristics, influencing factors, and prevention methods of air-entraining vortices. It discusses classification and development stages of vortices, focusing on their transition from surface swirl to fully developed air-core vortices. Special attention is given to the main factors that affect the formation and development of air-entraining vortices. The mechanism of gate vibration caused by air-entraining vortices is also examined. The paper also analyzes the effectiveness of various anti-vortex measures and identifies key research gaps, providing a valuable reference for future studies on vortex control and vibration mitigation in PSHPPs.