The development of technological devices, such as satellites and drones, has made it easier to collect images and videos from above. With rich and diverse data sources, the problem of detecting objects in aerial images is formed to serve real-life situations: rescue missions, social scenarios, security needs, and more. This issue attracts a lot of attention from researchers in computer vision because of its high applicability in real life. However, object detection in images collected from drones faces many significant challenges due to the complex factors of real-life environments. To overcome these difficulties, many studies focus on developing effective models for detecting and tracking objects from UAV systems. In this paper, our primary emphasis is comprehensive survey of methodologies pertaining to horizontal and oriented object detection. We analyzed and compared existing approaches such as CNN-based vs. Transformerbased, Anchor-based vs. Anchor-free. Moreover, we also learned about ways to represent objects using bounding boxes in oriented object detection. After researching many practical and innovative techniques in different approaches, we have carefully selected 15 methods for horizontal object detection and 18 for oriented object detection that were recently researched and developed to conduct classifications, surveys and assessments. We also provide a taxonomy mind map to assist readers in gaining an overview of the methods we surveyed. Additional, we examine 17 aerial image datasets collected from platforms and in various locations worldwide. These are typical datasets used to serve two primary tasks: Horizontal Object Detection and Oriented Object Detection. Then, we compared the experimental resultsof the previously introduced methods on four typical datasets: VisDrone, UAVDT, DOTAv1.0, and HRSC2016. The above datasets present diversity in the number of classes and the complexity of real-life conditions. Furthermore, they have been tested with various methods and shown remarkable results. For the reasons mentioned, we have enough basis to confirm that the comparison results are objective so that other research groups can make accurate comments and assessments on experimental methods on each dataset. We believe that updating and synthesizing the latest research will provide complete and comprehensive information, helping researchers to have more survey material for the development of the field of object detection in the future.INDEX TERMS aerial dataset, aerial image object detection, oriented object detection, and horizontal object detection.