  About 15 years ago, Bismut gave a natural construction of a Hodge theory for
a hypoelliptic Laplacian acting on the total space of the cotangent bundle of a
Riemannian manifold. This operator interpolates between the classical elliptic
Laplacian on the base and the generator of the geodesic flow. We will describe
recent developments of the theory of hypoelliptic Laplacians, in particular the
explicit formula obtained by Bismut for orbital integrals and the recent
solution by Shen of Fried's conjecture (dating back to 1986) for locally
symmetric spaces. The conjecture predicts the equality of the analytic torsion
and the value at 0 of the dynamic zeta function.
