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With the rapid development of object detection technology for unmanned aerial vehicles (UAVs), it is convenient to collect data from UAV aerial photographs. They have a wide range of applications in several fields, such as monitoring, geological exploration, precision agriculture, and disaster early warning. In recent years, many methods based on artificial intelligence have been proposed for UAV object detection, and deep learning is a key area in this field. Significant progress has been achieved in the area of deep-learning-based UAV object detection. Thus, this paper presents a review of recent research on deep-learning-based UAV object detection. This survey provides an overview of the development of UAVs and summarizes the deep-learning-based methods in object detection for UAVs. In addition, the key issues in UAV object detection are analyzed, such as small object detection, object detection under complex backgrounds, object rotation, scale change, and category imbalance problems. Then, some representative solutions based on deep learning for these issues are summarized. Finally, future research directions in the field of UAV object detection are discussed. [ABSTRACT FROM AUTHOR]