  We present our recent semi-analytical evaluation of the pion-pole
contribution to hadronic light-by-light scattering, using a description of the
pion-photon-photon form factor based on large-N_C and short-distance properties
of QCD. Inclusion of all light pseudoscalar states leads to a_{mu}(LbyL;PS) = +
8.3 (1.2) x 10^{-10}. We also sketch an effective field theory approach to
hadronic light-by-light scattering. It yields the leading logarithmic terms
that are enhanced by a factor N_C and shows that the sign of a_{mu}(LbyL;had)
cannot be inferred from a constituent quark-loop. In view of several
problematic issues that still remain to be clarified, our estimate for the full
hadronic light-by-light scattering contribution is a_{mu}(LbyL;had) = + 8 (4) x
10^{-10}.
