The Gauss-Manin system of a function is a direct image in the category of D-modules. For the case of isolated singularities there are two Singular libraries to compute it: gmssing.lib for (local) isolated hypersurface singularities, gmspoly.lib for (global) tame polynomial functions. In both cases the Gauss-Manin system carries a rich structure: an embedded (Brieskorn) lattice with an induced differential structure, a (Kashiwara-Malgrange) V-filtration, a monodromy operation defining a weight filtration, and a mixed Hodge structure. Resulting invariants like the spectral pairs belong to the finest known invariants of isolated hypersurface singularities. In the talk we focus on the case of tame polynomials to discuss the above structures and the main ideas behind the algorithmic methods to compute them.