  We will describe several pioneering efforts in the study of electromagnetic
radiative corrections to semileptonic decay processes, with particular emphasis
on the role of lattice QCD. These studies are essential for the precise
extraction of the matrix element $V_{ud}$ from beta decays of pion, free
neutron and $J^P=0^+$ nuclei, and are crucial to address several
recently-emerged anomalies involving $V_{ud}$ and $V_{us}$, which may provide
hints for physics beyond the Standard Model.
