This review paper explores the landscape of incipient fault detection methodologies within power distribution networks. It aims to provide insights into the current state-of-the-art techniques, their effectiveness, and potential avenues for future research. Incipient faults, often imperceptible and challenging to detect, pose significant risks to the stability and reliability of power distribution systems. Detecting these faults early ensures uninterrupted service and prevents catastrophic failures. The review begins by outlining the fundamental concepts of incipient faults and their implications on power distribution networks. It then surveys various detection methods, categorizing them into conventional and advanced techniques. Conventional methods include rule-based approaches, while advanced techniques encompass machine learning, artificial intelligence, and data-driven methodologies. Each category is examined in terms of its principles, advantages, and limitations. Furthermore, the review identifies key challenges and emerging trends in incipient fault detection, such as integrating smart grid technologies, utilizing big data analytics, and developing hybrid detection approaches. This thorough review enables stakeholders in the power distribution sector to enhance their comprehension of existing incipient fault detection techniques, thereby enabling informed decisions to enhance network reliability and resilience. Moreover, it offers invaluable insights for researchers and practitioners striving to drive advancements in the field through innovative methodologies and technologies.