Drinfeld introduced the notion of elliptic modules, which are now called Drinfeld modules, as an analogue of elliptic curves in the function field setting. To prove a Langlands correspondence, Drinfeld studied moduli spaces of elliptic sheaves. Since

then, many generalizations of elliptic sheaves have been studied, such as D-elliptic sheaves defined by Laumon, Rapoport, Stuhler and Frobenius-Hecke sheaves by Stuhler. In this talk, I will introduce a new generalization of elliptic sheaves, called

generalized D-elliptic sheaves. I will present some basic results on their moduli spaces, state a uniformization theorem and talk about the proof if time permits. This builds on work of Laumon-Rapoport-Stuhler, of Hartl and of Rapoport-Zink.