  We discuss the hadronic contributions to the muon anomalous magnetic moment.
They are dominated by light quark contributions which are constrained by the
mechanism of chiral symmetry breaking. Using the leading order result based on
$e^+ e^-$ scattering data, we show that the next-to-leading order contributions
in the fine structure constant $\alpha$ can be reliably calculated. Extending
this idea to the hadronic four-point function we give a prediction for the
light-by-light contribution.
