ABSTRACT: We will review the Geometric Langlands Conjecture, a non-abelian generalization of the theory of curves and their Jacobians. We will compare it to its arithmetic variants and discuss its overlap with homological mirror symmetry. We will then outline our program for proving GLC using non Abelian Hodge theory and Hitchin’s system. Finally, we will describe some recent results on the construction of automorphic sheaves in several specific cases.