  We review recent developments concerning the hadronic light-by-light
scattering contribution to the anomalous magnetic moment of the muon. We first
discuss why fully off-shell hadronic form factors should be used for the
evaluation of this contribution to the g-2. We then reevaluate the numerically
dominant pion-exchange contribution in the framework of large-N_C QCD, using an
off-shell pion-photon-photon form factor which fulfills all QCD short-distance
constraints, in particular, a new short-distance constraint on the off-shell
form factor at the external vertex in g-2, which relates the form factor to the
quark condensate magnetic susceptibility in QCD. Combined with available
evaluations of the other contributions to hadronic light-by-light scattering
this leads to the new result a_{\mu}(LbyL; had) = (116 \pm 40) x 10^{-11}, with
a conservative error estimate in view of the many still unsolved problems. Some
potential ways for further improvements are briefly discussed as well. For the
electron we obtain the new estimate a_{e}(LbyL; had) = (3.9 \pm 1.3) x
10^{-14}.
