  We report calculations of hadronic light-by-light scattering amplitudes via
lattice QCD evaluation of Euclidean four-point functions of vector currents.
These initial results include only the fully quark-connected contribution.
Particular attention is given to the case of forward scattering, which can be
related via dispersion relations to the $\gamma^* \gamma^* \to$ hadrons cross
section, and thus allows lattice data to be compared with phenomenology. We
also present a strategy for computing the hadronic light-by-light contribution
to the muon anomalous magnetic moment.
