Elliptic curves play a fundamental role in algebraic number theory. In the 1970’s Drinfeld defined analogues of elliptic curves in the function field setting, which are now called Drinfeld modules. Later on he defined a categorically equivalent notion, called elliptic sheaves, and studied their moduli space to prove Langlands correspondence. Since then many generalizations of Drinfeld modules and elliptic sheaves have been worked out. In the first part of this talk we will form the function field and classical setting and discuss similarities between them. Then, we define Drinfeld modules, discuss the analogy between elliptic curves and Drinfeld modules. In the second part we will define a new generalization of elliptic sheaves, called generalized D-elliptic sheaves and talk on their moduli space and of the uniformization of the latter if time permits.