Theoretical precision in estimates of the hadronic contributions to (g-2)_mu and alpha_QED(M_Z)

I review recent estimates of the non-perturbative hadronic vacuum polarization contributions. Since these at present can only be evaluated in terms of experimental data of limited precision, the related uncertainties pose a serious limitation in our ability to make precise predictions. Besides e+e- - annihilation data also tau decay spectra can help to get better predictions. Here, it is important to account for all possible iso-spin violations in tau - decay spectra, from which e+e- cross sections may be obtained by an iso-spin rotation. The observed 10% discrepancy in the region above the rho may be understood as a so far unaccounted iso-spin breaking effect.