Given a smooth Morse function and a Riemannian metric on a compact manifold, Witten defined a semiclassical operator which is now referred as the Witten Laplacian. In light of the recent developpement towards the spectral analysis of hyperbolic dynamical systems, I will discuss some well-known properties and some new ones of these Witten Laplacians. Namely, I will explain that the spectrum of these operators converges in the semiclassical limit to the so-called Pollicott-Ruelle spectrum. This is a joint work with N.V. Dang (Univ. Lyon 1).