The ongoing controversy regarding the Standard Model prediction of the muon anomalous magnetic moment makes necessary to better assess the accuracy of the relevant theoretical tools that are being employed. Three different determinations of the Adler function at low Euclidean values of Q^2 will be presented: 1) a theoretical QCD calculation, 2) a dispersive evaluation with e+e- data, and 3) a determination based on numerical lattice data. The lattice results turn out to be in very good agreement with the QCD expectations, while the dispersive estimates lie systematically below them. This comparison can be converted into an extraction of the strong coupling.While the lattice data imply a value of alpha_s in agreement with the FLAG average, the value extracted from e+e- data is between 1.5 and 2 sigma below it. This comparison confirms the trend already observed in g-2, with a systematic deficit of the e+e- estimate with respect to the lattice results of several groups. The potential impact of the very recent CMD-3 data will be also discussed.