With the rapid development and deep integration of unmanned aerial vehicle (UAV) and computer vision technologies, research on object detection in UAV aerial images has gained increasing attention and has been widely applied in precision agriculture, animal monitoring, urban management, emergency rescue, and other fields. Compared to images captured from conventional perspectives, images acquired by UAVs feature a wider field of view, significantly reduced object size, and variations in viewpoint and scale, rendering conventional object detection methods inadequate. Accordingly, a detailed review of progress in object detection methods from a conventional perspective was first provided, including traditional methods, deep learning methods, and large-model-based methods. Subsequently, the innovative strategies and optimization methods proposed by existing object detection methods were summarized, specifically addressing six challenging issues specific to UAV aerial image object detection, i.e., image quality degradation, scale and viewpoint variation, small-object detection difficulty, complex background and occlusion, imbalance in large fields of view, and high real-time requirements. Additionally, UAV aerial image object detection datasets were consolidated and analyzed, with an evaluation of the performance of existing methods on two representative datasets. Finally, potential research directions for the future were outlined based on the unresolved issues in the field of UAV aerial image object detection, providing reference for the development and application of object detection in UAV aerial images.