In this article, we give a first overview of the correspondence between Hermann Weyl and Erich Hecke during the 1930's. The translation and the analysis of some extracts from their letters will lead us to revisit several aspects of their respective trajectories : Weyl's recruitment at the University of Göttingen in 1930 ; the links that Weyl and the art historian Erwin Panofsky establish—because of their mutual friendship with Hecke—at the time of their exile at the Institute for Advanced Study, (IAS, Princeton) ; the situation that Hecke faces after 1933, while remaining professor at the University of Hamburg. In their correspondence, Weyl and Hecke refer to the crisis that the Deutsche Mathematiker Vereinigung is going through from 1934 onwards. They also mention their participation to the International Congress of Mathematicians which takes place in Oslo in 1936. Their correspondence finally contains some traces of the administrative difficulties that Hecke has to cope with before joining the IAS between January and May 1938.