  We review some recent progress in the theory of electroweak radiative
corrections in semileptonic decay processes. The resurrection of the so-called
Sirlin's representation based on current algebra relations permits a clear
separation between the perturbatively-calculable and incalculable pieces in the
$\mathcal{O}(G_F\alpha)$ radiative corrections. The latter are expressed as
compact hadronic matrix elements that allow systematic non-perturbative
analysis such as dispersion relation and lattice QCD. This brings substantial
improvements to the precision of the electroweak radiative corrections in
semileptonic decays of pion, kaon, free neutron and $J^P=0^+$ nuclei that are
important theory inputs in precision tests of the Standard Model. Unresolved
issues and future prospects are discussed.
