  We review the present status of the theoretical evaluation of the anomalous
magnetic moment of the the muon within the Standard Model. We mainly focus on
the hadronic contributions in the muon g-2 due to vacuum polarization effects,
light-by-light scattering and higher order electroweak corrections. We discuss
some recent calculations together with their uncertainties and limitations and
point out possible improvements in the future. In view of the inconsistent
values for the hadronic vacuum polarization based on e^+ e^- and tau data, no
conclusion can be drawn yet, whether the apparent discrepancy between the
current experimental and theoretical values for the muon g-2 points to physics
beyond the Standard Model.
