  These are the notes for the lecture given by the author at the "Current
Events" Special Session of the AMS meeting in Baltimore on January 17, 2003.
Topics reviewed include the Langlands correspondence for GL(n) in the function
field case and its proof by V.Drinfeld and L.Lafforgue, the geometric Langlands
correspondence for GL(n) and its proof by D.Gaitsgory, K.Vilonen and the
author, and the work of A.Beilinson and V.Drinfled on the quantization of the
Hitchin system and the Langlands correspondence for an arbitrary semisimple
algebraic group.
