This paper is an introduction to the (truncated) Hitchin fibration for a general reductive group. This fibration is the central object in the proofs of the fundamental lemma (by Ngô) and the weighted fundamental lemma (by Laumon and the author). We give also some explanations about the main cohomological result that is the key of our proofs. As an illustration of our methods, we sketch the proof of a relation between the cohomologies of Hitchin fibrations attached to the group $Sp(2n)$ and its dual group $SO(2n+1)$.