  We describe several techniques for the calculation of multi-loop integrals
and their application to heavy quark current correlators. As new results, we
present the four-loop correction to the second and third physical moment in the
low-energy expansions of vector, axial-vector and scalar quark current
correlators. Using a Ward identity, we obtain the third and fourth moment for
the pseudo-scalar correlator. We briefly discuss the impact of these results on
the determination of the charm quark mass and the strong coupling constant
using lattice simulations for the current correlators and of the charm- and
bottom-quark mass from experimental data for \sigma(e^+ e^- -> hadrons).
