  Calculations based on the analytic properties of the required matrix elements
allow for a wide range of applications constraining the hadronic contributions
to the anomalous magnetic moment of the muon $a_\mu=(g-2)_\mu/2$, both hadronic
vacuum polarization (HVP) and hadronic light-by-light (HLbL) scattering. Here,
we discuss such recent applications, including analyticity constraints on
hadronic cross sections, radiative corrections, and isospin-breaking effects.
