Abstract: Spurred by the rapid integration of unmanned aerial vehicles (UAVs) in modern military missions, significant research has been performed in the field of autonomous aerial refueling with a focus on the detection, control, and guidance of the tanker and receiver. The concept of aerial refueling has been highly valued in the military since it was first proposed in 1917. Through aerial refueling, an aircraft can significantly expand its combat range, extend its flight time, and improve its carrying capacity; thus, its combat effectiveness can be greatly improved. Furthermore, aerial refueling is gradually showing its merits in the civil domain; for example, it can be used to increase the travel distance of postal aircraft. There are two main types of aerial refueling: flying boom refueling (FBR) and probe-drogue refueling (PDR). Compared with FBR, PDR meets the requirements of UAVs such as high flexibility, high safety, and simplicity. Thus, PDR is more suitable than FBR for unmanned aerial systems. Unique advantages of PDR have allowed it to become the most extensively used refueling method, and the study of PDR has attracted increasing attention. However, the most important and complicated part in such studies is the modeling and control design of a refueling hose system. This paper described the results of a study conducted on the modeling and control design of PDR. First, this paper summarized the main types of aerial refueling and analyzed the characteristics of PDR. Subsequently, two types of modeling of PDR were introduced: lumped parameter system and distributed parameter system. Next, based on the modeling of the aerial refueling hose system, the control design of docking control, vibration control, and controllable drogue was analyzed for the entire process of aerial refueling. Finally, avenues for future research on the modeling and control design of PDR such as the accuracy of the model, complexity of the control system, and details of the working environment at various altitudes were discussed.