Variations on Photon Vacuum Polarization

I provide updates for the theoretical predictions of the muon and electron anomalous magnetic moments, for the shift in the fine structure constant $\alpha (M_Z)$ and for the weak mixing parameter ${\sin }^2{\mathrm{\Theta }}_W(M_Z)$. Phenomenological results for Euclidean time correlators, the key objects in the lattice QCD approach to hadronic vacuum polarization, are briefly considered. Furthermore, I present a list of isospin breaking and electromagnetic corrections for the lepton moments, which may be used to supplement lattice QCD results obtained in the isospin limit and without the e.m. corrections.