In this talk, I will give an overview of the status of our theoretical
understanding of the muon anomalous magnetic moment. I will
then focus on the contribution of the hadronic vacuum polarization,
for which significant discrepancies between "data-driven" estimates
based on cross-section data for electrons-positrons to hadrons and lattice
computations are emerging. In the latter part, I will concentrate on
the discrepancy between data-driven and lattice-based values for
the light-quark connected part of the so-called RBC/UKQCD window
quantity, which constitutes a part of the hadronic vacuum polarization
for which very precise estimates are available.