The hadronic vauum polarization contribution to the muon anomalous magnetic moment

In this talk, I will review aspects of Standard-Model estimates of the anomalousmagnetic moment of the muon. The largest part of the uncertainties in these estimates come from hadronic contributions, in particular the hadronic vacuum polarization (HVP) contribution, which will be the topic of my talk. These contributions have been computed using both lattice QCD and experimental data such as $e^+e^-\to$~hadrons through dispersive methods. I will focus on the comparison between lattice and dispersive results, as well as discrepancies and puzzles within the data-based approach.