The rapid development of uncrewed aerial vehicles (UAVs) has significantly increased their usefulness in various fields, particularly in remote sensing. This paper provides a comprehensive review of UAV path planning, obstacle detection, and avoidance methods, with a focus on its utilisation in both single and multiple UAV platforms. The paper classifies the algorithms into two main categories: (1) global and local path-planning approaches in single UAVs; and (2) multi-UAV path-planning methods. It further analyses obstacle detection and avoidance methods, as well as their capacity to adapt, optimise, and compute efficiently in different operational environments. The outcomes highlight the advantages and limitations of each method, offering valuable information regarding their suitability for remote sensing applications, such as precision agriculture, urban mapping, and ecological surveillance. Additionally, this review also identifies limitations in the existing research, specifically in multi-UAV frameworks, and provides recommendations for future developments to improve the adaptability and effectiveness of UAV operations in dynamic and complex situations.