The local Langlands correspondence for GSp(4)
gives a classification of irreducible complex representations of GSp(4,k),
where k is a p-adic field in terms of 4-dimensional symplectic
Galois representations (plus some additional data). I will describe the
precise statement and give an idea of its proof. I will also mention
some further questions in this direction. This is joint work with
Shuichiro Takeda.