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EVALUATION OF α(M2 Z) AND (g − 2)µ

This talk summarizes the recent development in the evaluation of the leading order hadronic contributions to the running of the QED fine structure constant α(s), at s = M 2 Z , and to the anomalous magnetic moments of the muon (g − 2)µ. The accuracy of the theoretical prediction of these observables is limited by the uncertainties on the hadronic contributions. Significant improvement has been achieved in a series of new analyses which is presented historically in three steps: (I), use of τ spectral functions in addition to e + e − cross sections, (II), extended use of perturbative QCD and (III), application of QCD sum rule techniques.