Abstract: The muon's anomalous magnetic moment, a_μ, holds special significance in the development of the Standard Model (SM). Precise calculations and measurements of this quantity provide a stringent test of the SM and a window to the physics beyond. The new Fermilab measurements from Run-1/2/3 increase the discrepancy with respect to the SM prediction obtained in the Muon g-2 Theory Initiative WP of 2020 at the 5σ level. However, recent results for the hadronic vacuum polarization (HVP) contribution, which dominates the overall uncertainty, are in tension with the previous estimation in the dispersive approach and predict a number closer to the experimental average. In this talk, I will discuss the use of hadronic tau decays as a supplementary tool for calculating the HVP integrals, and how they could help us address these tensions.