Cavitation is a detrimental phenomenon in hydraulic machinery, adversely impacting its performance, inducing vibration and noise, and leading to corrosion damage of overflow components. Centrifugal pump internal cavitation will lead to severe vibration and noise, and not only will the performance of hydraulic machinery be adversely affected but the impact generated by the collapse of the vacuole will also cause damage to the impeller wall structure, seriously affecting the safety of the equipment’s operation. To prevent the generation and development of internal cavitation in centrifugal pumps, to prevent the hydraulic machinery from being in a state of cavitation for a long time, to avoid the failure of the unit, and to realize the predictive maintenance of centrifugal pumps, therefore, it is of great significance to research the methods for monitoring the cavitation of hydraulic machinery and the methods for suppressing the cavitation. This paper comprehensively describes the centrifugal pump cavitation mechanism and associated hazards. It also discusses the current state of centrifugal pump cavitation monitoring methods, including commonly used approaches such as the flow-head method, high-speed photography, pressure pulsation method, acoustic emission method, and vibration method. A comparative analysis of these methods is presented. Additionally, the paper explores signal characterization methods for centrifugal pump cavitation, including time-domain feature extraction, frequency-domain feature extraction, and time–frequency-domain feature extraction. The current research status is elaborated upon. Moreover, the paper presents methods to mitigate cavitation and prevent its occurrence. Finally, it summarizes the ongoing research on identifying and determining the cavitation state in centrifugal pumps and offers insights into future research directions.