The increasing prevalence of unmanned aerial vehicles (UAVs) across various fields requires the development of advanced fault detection and diagnostic (FDD) frameworks to prevent the severe consequences of undetected sensor and actuator failures. This review investigates the wide spectrum of FDD methodologies for UAVs, focusing on the paramount role of sophisticated yet intelligent systems in safeguarding operational integrity, particularly in near-human environments. An analysis of 32 seminal publications from well-recognized databases presents a trend towards converging signal processing and machine learning techniques using UAV specific fault detection keywords. This analysis underscores the trend of data-driven models capable of performing real-time diagnostics. The authors increase interest in hybrid methodologies that correlate the precision of signal processing and the adaptive nature of machine learning. These approaches aim to gain fault detection accuracy and achieve better prognostic capabilities. By deconstructing the strengths and weaknesses of various methods, this analysis concludes with the need for further research into upcoming new challenges. The review focuses on the investigation of synergistic strategies and encourages interdisciplinary collaboration for advancements in FDD methods. These initiatives will enhance UAV safety and reliability across a wide range of operational contexts.