  We describe two recent developments of the radiative correction theory in
semileptonic beta decays. For neutron, a novel dispersive analysis of the
$\gamma W$-box diagram making use of neutrino scattering data leads to an
improved precision and a shifted central value of $V_{ud}$; for kaon, an
appropriate combination of meson form factors, lattice QCD inputs and chiral
perturbation theory gives a much-improved determination of the radiative
corrections in semileptonic kaon decays. These new calculations help to
unveil/sharpen a series of anomalies in the measurements of $V_{ud}$ and
$V_{us}$ that may point towards the existence of new physics.
