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First a brief overview of C. Possio's short but outstanding and fruitful carreer is given. This is followed by an outline of the state of the art in flutter and unsteady aerodynamic research, and of the challenges and problems arising in aircraft development at that time, like high speed flight. His first publications until 1937 about gas dynamic and supersonic problems are reviewed. Main focus is put on his 1938 report about unsteady subsonic compressible 2D flow, which became famous and was named after him, because he was the first one who developed an unsteady compressible aerodynamic theory, which was so urgently needed in those years. The theory, based on Prandtl's acceleration potential is briefly outlined. Some discussions and comments in Germany and other countries at that time highlight the importance of this work for the scientific community. Early solutions of Possio's integral equation by himself and later ones by other researchers are presented, as well as the following approaches to extend the theory to 3 dimensional flows before the war, like Kuessner's theory, which was probably influenced by Possio. Finally C. Possio's later scientific contributions to windtunnel interference and to hydrodynamics are sketched. Summarising some developments of the 2nd half of the 20th century, which are based on Possio’s work, demonstrate, that C. Possio created a milestone for modern aircraft research during his very short carreer.