  The muon anomalous magnetic moment is one of the most precisely measured
quantities in particle physics. Recent high precision measurements (0.54ppm) at
Brookhaven reveal a ``discrepancy'' by 3 standard deviations from the
electroweak Standard Model which could be a hint for an unknown contribution
from physics beyond the Standard Model. This triggered numerous speculations
about the possible origin of the ``missing piece''. The remarkable 14-fold
improvement of the previous CERN experiment, actually animated a multitude of
new theoretical efforts which lead to a substantial improvement of the
prediction of a_mu. The dominating uncertainty of the prediction, caused by
strong interaction effects, could be reduced substantially, due to new hadronic
cross section measurements in electron-positron annihilation at low energies.
After an introduction and a brief description of the principle of the
experiment, I present a major update and review the status of the theoretical
prediction and discuss the role of the hadronic vacuum polarization effects and
the hadronic light--by--light scattering contribution. Prospects for the future
will be briefly discussed. As, in electroweak precision physics, the muon g-2
shows the largest established deviation between theory and experiment at
present, it will remain one of the hot topics for further investigations.

High Energy Physics - Phenomenology