  We summarize our recent new evaluation of the pion-exchange contribution to
hadronic light-by-light scattering in the muon g-2. We first derive a new
short-distance constraint on the off-shell pion-photon-photon form factor at
the external vertex in a_\mu which relates the form factor to the quark
condensate magnetic susceptibility in QCD. We then evaluate the pion-exchange
contribution in the framework of large-N_C QCD using an off-shell form factor
which fulfills all short-distance constraints and obtain the new estimate
a_{\mu}(LbyL;\pi^0) = (72 \pm 12) x 10^{-11}. Updating our earlier results for
the contributions from the exchanges of the eta and eta-prime using simple
vector-meson dominance form factors, we get a_{\mu}(LbyL; PS) = (99 \pm 16) x
10^{-11} for the sum of all light pseudoscalars. Combined with available
evaluations for the other contributions to hadronic light-by-light scattering
this leads to the estimate a_{\mu}(LbyL; had) = (116 \pm 40) x 10^{-11}. The
corresponding contributions to the anomalous magnetic moment of the electron
are also given.
