  In this paper, we discuss spectral properties of Laplacians associated with
an arbitrary smooth distribution on a compact manifold. First, we give a survey
of results on generalized smooth distributions on manifolds, Riemannian
structures and associated Laplacians. Then, under the assumption that the
singular foliation generated by the distribution is regular, we prove that the
Laplacian associated with the distribution defines an unbounded multiplier on
the foliation $C^*$-algebra. To this end, we give the construction of a
parametrix.
