Dispersive approaches for the HVP and HLbL contributions to $(g-2{)}_{\mu }$

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 $a_{\mu }=(g-2{)}_{\mu }\mathrm{/}2$, 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.