Aircraft systems are designed to perform functions that will aid the various missions of the aircraft. Their performance, when subjected to an unfamiliar condition of operation, imposes stress on them. The system components experience degradation due to fault which ultimately results in failure. Maintenance and monitoring mechanisms are put in place to ensure these systems are readily available when required. Thus, the sensing of parameters assists in providing conditions under which healthy and faulty scenarios can be indicated. To obtain parameter values, sensor data is processed, and the results are displayed so that the presence of faults may be known. Some faults are intermittent and incipient in nature. These are not discovered easily and can only be known through a display of unusual system performance by error code indication. Therefore, the assessed faults are transmitted to a maintenance crew by error codes. The results may be fault found (FF), no fault found (NFF), or cannot display (CND). However, the main classification of the faults and their origins may not be known in the system. This continues throughout the life cycle of the system or equipment. This paper reviews the diagnostic methods used for the hydraulically powered flight control actuation system (HPFCAS) of an aircraft and its interaction with other aircraft systems. The complexities of the subsystem’s integration are discussed, and different subsystems are identified. Approaches used for the diagnostics of faults, such as model-based, statistical mapping and classification, the use of algorithms, as well as parity checks are reviewed. These are integrated vehicle health management (IVHM) tools for systems diagnostics. The review shows that when a system is made up of several subsystems on the aircraft with dissimilar functions, the probability of fault existing in the system increases, as the subsystems are interconnected for resource sharing, space, and weight savings. Additionally, this review demonstrates that data-driven approaches for the fault diagnostics of components are good. However, they require large amounts of data for feature extraction. For a system such as the HPFCAS, flight-management data or aircraft maintenance records hold information on performance, health monitoring, diagnostics, and time scales during operation. These are needed for analysis. Here, a knowledge of training algorithms is used to interpret different fault scenarios from the record. Thus, such specific data are not readily available for use in a data-driven approach, since manufacturers, producers, and the end users of the system components or equipment do not readily distribute these verifiable data. This makes it difficult to perform diagnostics using a data-driven approach. In conclusion, this paper exposes the areas of interest, which constitute opportunities and challenges in the diagnostics and health monitoring of flight-control actuation systems on aircraft.