The discipline of Aeroelasticity comprises physical phenomena, which occur on structures in an airflow, when the aerodynamic forces interact with the elastomechanical forces in the structure. Aeroelastic effects occur for example on plants or on buildings in free airflow. For aircraft however, aeroelastic stability is of exceptional importance: due to the necessary extreme lightweight design, aircraft have relatively flexible structures. As a consequence, aeroelastic deformations and oscillations can cause severe problems for the aircraft behavior. Already the Wright brothers were confronted with aeroelastic problems: they found solutions more by intuition than by identification of the physical mechanisms. In Göttingen, scientific research is done since the 1920s already: publications of L. Prandtl, W. Birnbaum, H. Wagner, H.G. Küssner, H. Blenk and P. Jordan found international attraction and can be seen therefore as important milestones in the progress of Aircraft Aeroelasticity. Founded in 1957, the former AVA department for Aeroelasticity became a separate institute after integration of the AVA into the DFVLR. It is the only research institute of the kind in Europe. In the institute multidisciplinary research activities and industrial contracts are performed with the aim to reliably predict aeroelastic phenomena and to ensure therefore operational safety of new developments. Experimental and numerical methods are developed and used for these analyses. In the last decade the research work was focussed on nonlinearities in the aeroelastic behaviour of transport aircraft. Other important research fields concern the Aeroelasticity of turbomachines and rotorcrafts. Corresponding to the Europeanization of the aeronautical industry, the institute cooperates intensively with the French aerospace research center ONERA.