A singular foliation $F$ on a complete Riemannian manifold $M$ is said to be Riemannian if each geodesic that is perpendicular at one point to a leaf remains perpendicular to every leaf it meets . The singular foliation is said to admit sections if each regular point is contained in a totally geodesic complete immersed submanifold that meets every leaf orthogonally and whose dimension is the codimension of the regular leaves. A typical example of a singular Riemannian foliation with section (s.r.f.s for short) is the partition by orbits of a polar action, i.e. a proper isometric action which admit sections. The most well known example is the partition by orbits of the adjoint action of a compact Lie group on itself. Other examples of s.r.f.s are the partition formed by parallel submanifolds of an isoparametric submanifold and examples constructed by suspension of homomorphism, suitable changes of metric and surgery. In this talk we review some author's results about singular holonomy of s.r.f.s and also some results of a joint work with Toeben and a joint work with Gorodski.