  Let $f : X -> B$ be a projective surjective morphism between quasi-projective
varieties. The goal of this paper is the study of the Chow groups of $X$ in
terms of the Chow groups of $B$ and of the fibers of $f$. One of the
applications concerns quadric bundles. When $X$ and $B$ are smooth projective
and when $f$ is a flat quadric fibration, we show that the motive of $X$ is
"built" from the motives of varieties of dimension less than the dimension of
$B$.
