The anomalous magnetic moment of the muon has served over many decades as
an important test of the Standard Model. It is also sensitive to
contributions from New Physics around the electroweak scale. Indeed, for
the last few years, a discrepancy of more than three standard deviations
has been observed between the theoretical prediction in the Standard Model
and the measured value. In this talk, we first briefly review the various
contributions to the muon g-2 and then focus on recent developments
concerning the hadronic contributions which yield the largest uncertainty
in the theoretical prediction. We then discuss in detail the hadronic
light-by-light scattering contribution. In contrast to the hadronic vacuum
polarization correction, this contribution cannot be related to a
measurable quantity like a hadronic cross section and therefore one has to
rely on models to evaluate it. In order to reduce this model dependence,
we present a new QCD short-distance constraint on the numerically dominant
pion-exchange contribution and evaluate it in the framework of large N_C
QCD. We comment on the status of the other contributions in hadronic
light-by-light scattering and give an outlook on how further improvements
could be achieved by combining theoretical and experimental constraints on
the relevant hadronic form factors. Finally, we present our new estimate
for the muon g-2 in the Standard Model.