To implement Prognostics Health Management (PHM) for hydraulic pumps, it is very important to study the faults of hydraulic pumps to ensure the stability and reliability of the whole life cycle. The research on fault diagnosis has been very active, but there is a lack of systematic analysis and summary of the developed methods. To make up for this gap, this paper systematically summarizes the relevant methods from the two aspects of fault diagnosis and health management. In addition, in order to further facilitate researchers and practitioners, statistical and comparative analysis of the reviewed methods is carried out, and a future development direction is prospected.