  The recent precise measurement of the muon magnetic anomaly (g-2)_{mu} at BNL
opens a window into possible new physics, provided the contribution from
hadronic vacuum polarization is well understood. This talk summarizes the
development in the evaluation of the leading order hadronic contributions.
Significant improvement has been achieved in a series of analyses which is
presented historically in three steps: (1), use of tau spectral functions in
addition to e+e- cross sections, (2), extended use of perturbative QCD and (3),
application of QCD sum rule techniques. The uncertainties, in particular
concerning the CVC hypothesis used in step (1), and global quark-hadron duality
employed in steps (2) and (3) are discussed. No new analysis results are given
in these proceedings.
