In the first part of the talk, I will give a quick introduction to $D$-modules, local cohomology, s-parametric annihilators and Bernstein-Sato polynomials. In the second part, I will consider holonomic $D$-modules associated to a hypersurface with non-isolated singularities. I will show a method for computing holonomic $D$-modules and microlocal b-functions. The keys of the method are the use of a Poincare-Birkhoff-Witt algebra and local cohomology. I will discuss, as applications, relations between the structure of holonomic $D$-module and the vertical monodromy introduced by Siersma and Le cycles introduced by Massey.