On some synthetic curvature conditions in sub-Riemannian geometry

In recent years there has been much interest in generalizing the notion of Ricci curvature to spaces more general than Riemannian manifolds. In one direction some differential invariants generalizing the Ricci tensor have been introduced for subriemannian manifold. On the other hand, much work has been done to define curvature-like quantities for general metric spaces with a measure, without requiring a differentiable structure. In this thesis we review some of this topics with a special interest in the interplay between synthetic notions of curvature and subriemannian geometry.