Suppose R=KK[x_1,...,x_n] is a polynomial ring over a field KK of characteristic zero. If I is an ideal in R, then the local cohomology modules H^j_I(R) can be computed (at least in principle) in Macaulay2. In this talk we discuss the basic ideas that go into this (Groebner basis driven) algorithm. This involves a tour through the land of D-modules, with specific focus on the concept of Bernstein—Sato polynomials attached to elements f of R (which we will define and discuss).