  I review recent evaluations of the hadronic contributions to the muon
anomalous magnetic moment (g-2)_mu and to the effective fine structure constant
alpha (M_Z). A new estimate for the hadronic shift delta_alpha hadronic =
0.027782 +/- 0.000254 is presented which implies 1/alpha (M_Z) = 128.913 +/-
0.035. It is based on a recent perturbative calculation of the Adler function
which includes mass effects up to three-loops in a MOM scheme and requires
little ad hoc assumptions. I then discuss perspectives for possible
improvements in estimations of g-2 which we expect from the Phi--factory DAPHNE
at Frascati.
