Maintaining obstacle-free runways is an essential part of airport operations and aviation safety. The growing availability of high-resolution imagery from UAVs, especially from publicly available datasets like the Stanford Drone Dataset (SDD), presents new challenges and opportunities for innovative obstacle detection systems. This paper provides a systematic methodological overview of airport runway obstacle detection from UAV imagery with emphasis on methods transferable to the SDD. This methodology examines cutting-edge computer vision methods, among them object recognition models like YOLO, Faster R-CNN, and Vision Transformers, and their theoretical potential for recognizing common runway hazards like cars, people, and foreign object debris (FOD). The review also contains a thorough analysis of the SDD's architecture, objects, resolution, and limitations relative to runway conditions. We also introduce a conceptual pipeline for real-time obstacle detection and discuss its possible incorporation into airport safety management systems. Lastly, this review determines the main research gaps and presents future research directions for enhancing obstacle detection accuracy, real-time performance, and adaptability to varied airport environments. This work intends to provide a basis for future experimental studies and system development utilizing UAV-based imagery for airport runway safety.