Geophysical surveys, a conventional means of analyzing the Earth and its environs, have traditionally relied on ground-based methodologies. However, up-to-date approaches encompass remote sensing (RS) techniques, employing both spaceborne and airborne platforms. The emergence of Unmanned Aerial Vehicles (UAVs) has notably catalyzed interest in UAV-borne geophysical RS. This study comprehensively reviews the state-of-the-art UAV-based geophysical methods, encompassing magnetometry, gravimetry, gamma-ray spectrometry/radiometry, electromagnetic (EM) surveys, ground penetrating radar (GPR), traditional UAV RS methods (i.e., photogrammetry and LiDARgrammetry), and integrated approaches. Each method is scrutinized concerning essential aspects such as sensors, platforms, challenges, applications, etc. Drawing upon an extensive review of over 435 scholarly works, our analysis reveals the versatility of these systems, ranging from geophysical development to applications over various geoscientific domains. The reviewed studies unanimously highlight the advantages of UAV RS in geophysical surveys. UAV geophysical RS effectively balances the benefits of ground-based and traditional RS methods regarding cost, resolution, accuracy, and other factors. Integrating multiple sensors on a single platform and fusion of multi-source data enhance efficiency in geoscientific analysis. However, implementing geophysical methods on UAVs poses challenges, prompting ongoing research and development efforts worldwide to find optimal solutions from both hardware and software perspectives.