  Quantum loops induce an anomaly, a_mu, in the magnetic moment of the muon
that can be accurately measured. Its Standard Model prediction is limited in
precision by contributions from hadronic vacuum polarisation of the photon. The
dominant lowest-order hadronic term can be calculated with a combination of
experimental cross section data, involving e+e- annihilation to hadrons, and
perturbative QCD. These are used to evaluate an energy-squared dispersion
integral that strongly emphasises low photon virtualities. The dominant
contribution to the integral stems from the two-pion channel that can be
measured both in e+e- annihilation and in tau decays. The corresponding e+e-
and tau-based predictions of a_mu exhibit deviations by, respectively, 3.6
sigma and 2.4 sigma from experiment, leaving room for a possible interpretation
in terms of new physics. This talk reviews the status of the Standard Model
prediction with emphasis on the lowest-order hadronic contribution. Also given
is the latest result for the running electromagnetic fine structure constant at
the Z-mass pole, whose precision is limited by hadronic vacuum polarisation
contributions, determined in a way similar to those of the magnetic anomaly.
