  The muon anomalous magnetic moment is one of the most precisely measured
quantities in particle physics. In a recent experiment at Brookhaven it has
been measured with a remarkable 14-fold improvement of the previous CERN
experiment reaching a precision of 0.54ppm. Since the first results were
published, a persisting "discrepancy" between theory and experiment of about 3
standard deviations is observed. It is the largest "established" deviation from
the Standard Model seen in a "clean" electroweak observable and thus could be a
hint for New Physics to be around the corner. This deviation triggered numerous
speculations about the possible origin of the "missing piece" and the increased
experimental precision animated a multitude of new theoretical efforts which
lead to a substantial improvement of the prediction of the muon anomaly
a_mu=(g_mu-2)/2. 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. Also
the recent electron g-2 measurement at Harvard contributes substantially to the
progress in this field, as it allows for a much more precise determination of
the fine structure constant alpha as well as a cross check of the status of our
theoretical understanding.
