  This paper is a proceedings version of \cite{CHT-I}, in which we state a
Quantum Ergodicity (QE) theorem on a 3D contact manifold, and in which we
establish some properties of the Quantum Limits (QL). We consider a
sub-Riemannian (sR) metric on a compact 3D manifold with an oriented contact
distribution. There exists a privileged choice of the contact form, with an
associated Reeb vector field and a canonical volume form that coincides with
the Popp measure. We state a QE theorem for the eigenfunctions of any
associated sR Laplacian, under the assumption that the Reeb flow is ergodic.
The limit measure is given by the normalized canonical contact measure. To our
knowledge, this is the first extension of the usual Schnirelman theorem to a
hypoelliptic operator. We provide as well a decomposition result of QL's, which
is valid without any ergodicity assumption. We explain the main steps of the
proof, and we discuss possible extensions to other sR geometries.
