g−2 of the muon and Δα re-evaluated

We briefly review the Standard Model prediction of g−2 of the muon and confront it with the formidably accurate measurement from BNL. The focus is on recent improvements of the hadronic vacuum polarisation contributions. We also calculate the running QED coupling at space- and time-like momentum transfer. Its value at the scale of the Z boson mass, , is an important ingredient in electroweak precision fits and its prediction is improved considerably.