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Unmanned Aerial Vehicles (UAV) have been widely used due to their advantages of small size, light weight, and simple operation. The combination of the deep learning method and UAV system can help to quickly and accurately detect the desired target on UAV aerial images with high definition and a wide field of view. Related topics have become one of the current research hotspots. This paper reviews the research progress of deep learning methods for object detection and semantic segmentation in UAV aerial images in the past ten years. First, the characteristics and wide range of application scenarios of UAVs and their aerial images are summarized, and the development process of target detection and semantic segmentation methods for UAV aerial images is briefly described. Then, the object detection and semantic segmentation methods of UAV aerial images based on deep learning are classified according to different network models, and their improvement strategies, application scenarios, contributions, and limitations are summarized. Subsequently, the data sets of aerial images taken by UAVs in recent years are collected and sorted out, and the evaluation indicators of commonly used convolutional neural network models are summarized. Finally, the existing problems in this field are pointed out, and prospects for future research trends are presented.