Abstract Flying-wing aircraft with high-aspect ratios have received extensive attention due to their outstanding aerodynamic efficiency and stealth capabilities. This type of aircraft, however, may suffer from rigid-elastic coupling flutters, such as a body-freedom flutter, owing to the interaction among flight dynamics, structural dynamics, and aerodynamics. This paper surveys the advances in modeling and analysis methods, control strategies, and experimental validations related to those flutters and their active suppressions. The paper begins with the modeling approaches in different frames of reference for a rigid-elastic coupling aero-servo-elastic system to emphasize their roles and merits in describing rigid-elastic interactions. Then, it discusses the mechanism of a rigid-elastic coupling flutter, accounting for the coupling of flight dynamics and aeroelastic vibrations. Afterward, the paper presents a comparison among the control performances of typical active flutter suppression strategies to evaluate the capacity of enhancing aircraft stability and increasing flutter speed. The paper also reviews the wind-tunnel tests and flight tests to verify the active flutter suppression techniques. Unlike other tests, the flight tests of the aeroelastic flight demonstrator (AFD) made by the authors indicate that the active controller could successfully remove the rigid-elastic coupling flutter and greatly increase the flutter speed till the occurrence of a bending-torsion flutter of higher order. Finally, the paper outlines future studies on flying-wing aircraft and active flutter suppression techniques.