In this talk we will present some properties of the motion by curvature in subriemannian setting. This describes the motion of a surface when each point is moving in the normal direction with speed proportional to the mean curvature. The problem is well undestood in Riemannian setting, while only partial results are known in the subriemannian one, due to the presence of characteristic points of the evolving surface. In order to avoid the problem solutions can be found as limit of the riemannian approximation. We present here some existence and uniqueness results for these type of solutions, obtained in collaboration with E. Baspinar, and some application to image completion obtained in collaboration with Franceschello, Sanguinetti and Sarti.