  The global geometric Langlands correspondence relates Hecke eigensheaves on
the moduli stack of G-bundles on a smooth projective algebraic curve X and
holomorphic G'-bundles with connection on X, where G' is the Langlands dual
group of G. This correspondence is relatively well understood when the
connection has no singularities, i.e., is unramified. But what should happen if
the connection has singularities, or ramification, at finitely many points of
X? In this case we expect to attach to it a category of Hecke eigensheaves on a
suitable moduli stack of G-bundles on X with parabolic (or level) structures at
the ramification points. In this paper I review an approach to constructing
these categories developed by D.Gaitsgory and myself. It uses representations
of affine Kac-Moody algebras of critical level and localization functors from
these representations to D-modules on the moduli spaces of bundles with
parabolic (or level) structures. As explained in hep-th/0512172, these
D-modules may be viewed as sheaves of conformal blocks naturally arising in the
framework of Conformal Field Theory.
