  We think that phenomenological resonance Lagrangian models, constrained by
global fits from low energy hadron reaction data, can help to improve muon g-2
predictions. The main issue are those contributions which cannot be calculated
by perturbative means: the hadronic vacuum polarization (HVP) effects and the
hadronic light--by--light (HLbL) scattering contribution. I review recent
progress in the evaluation of the HVP contribution within the broken Hidden
Local Symmetry (HLS) framework, worked out in collaboration with M. Benayoun,
P. David and L. DelBuono. Our HLS driven estimate reads a_mu (LO
had)=(688.60+\-4.24) 10^{-10} and we find a_mu (theory)= (11 659 177.65 +/-
5.76) 10^{-10}.
