  We review the approach to the geometric Langlands program for algebraic
curves via S-duality of an N=4 supersymmetric four dimensional gauge theory,
initiated by Kapustin and Witten in 2006. We sketch some of the central further
developments. Placing this four dimensional gauge theory into a six dimensional
framework, as advocated by Witten, holds the promise to lead to a formulation
which makes geometric Langlands duality a manifest symmetry (like coavariance
in differential geometry). Furthermore, it leads to an approach toward
geometric Langlands duality for algebraic surfaces, reproducing and extending
the recent results of Braverman and Finkelberg.
