A morphing aircraft can adapt its configuration to suit different types of tasks, which is also an important requirement of Unmanned Aerial Vehicles (UAV). The successful development of an unmanned morphing aircraft involves three steps that determine its ability and intelligent: configuration design, dynamic modeling and flight control. This study conducts a comprehensive survey of morphing aircraft. First, the methods to design the configuration of a morphing aircraft are presented and analyzed. Then, the nonlinear dynamic characteristics and aerodynamic interference caused by a morphing wing are described. Subsequently, the dynamic modeling and flight control methods for solving the flight control problems are summarized with respect to these features. Finally, the general as well as special challenges ahead of the development of intelligent morphing aircraft are discussed. The findings can provide a theoretical and technical reference for designing future morphing aircraft or morphing-wing UAVs.