The geometric Langlands conjecture is an analogue of the Langlands correspondence in number theory, in which number fields are replaced by Riemann surfaces and the Galois group is replaced by the fundamental group. I will explain the analogy and some motivation behind this conjecture and give some indication of the proof. This is based on joint work with Arinkin, Beraldo, Campbell, Chen, Faergeman, Gaitsgory, Lin, and Raskin.