Despite the tremendous progress made during the 50 years since they were formulated, the Langlands conjectures remain mysterious until today.  The conjectures, in their original form, relate finite dimensional representations of the absolute Galois group of to certain -packets of automorphic representations of the adele groups , for arbitrary reductive groups over . This relationship should be, in a very precise way, controlled  by a coincidence of -series, and similarly of -factors, attached to respectively . Furthermore,  it is supposed that the correspondence respects the local-global principle. The analogous local Langlands conjecture, linking finite dimensional representations of the absolute Galois groups for completions of to smooth irreducible  representations of , has been proved by Harris, Taylor and Henniart for the groups in 2001. However, beyond this not much is known for arbitrary .  We give a survey on this, including a discussion of some recent results on the Langlands correspondence in the case .