  Nonperturbative QCD corrections are important to many low-energy electroweak
observables, for example the muon magnetic moment. However, hadronic
corrections also play a significant role at much higher energies due to their
impact on the running of standard model parameters, such as the electromagnetic
coupling. Currently, these hadronic contributions are accounted for by a
combination of experimental measurements, effective field theory techniques and
phenomenological modeling but ideally should be calculated from first
principles. Recent developments indicate that many of the most important
hadronic corrections may be feasibly calculated using lattice QCD methods. To
illustrate this, we will examine the lattice computation of the leading-order
QCD corrections to the muon magnetic moment, paying particular attention to a
recently developed method but also reviewing the results from other
calculations. We will then continue with several examples that demonstrate the
potential impact of the new approach: the leading-order corrections to the
electron and tau magnetic moments, the running of the electromagnetic coupling,
and a class of the next-to-leading-order corrections for the muon magnetic
moment. Along the way, we will mention applications to the Adler function,
which can be used to determine the strong coupling constant, and QCD
corrections to muonic-hydrogen.
