Semi-leptonic processes involving pions are used to test the Standard Model with high precision. On the theory side, the evaluation of radiative corrections is a crucial ingredient for a robust comparison between theoretical predictions and experimental measurements. In this talk, I will present the first complete effective field theory treatment of radiative corrections in pion $\beta$ decay ($\pi^{\pm} \rightarrow \pi^0 \, e \, \nu_{e}$) and $\tau^{\pm} \rightarrow \pi^{\pm} \, \pi^{0} \, \nu_{\tau}$ beyond leading-logarithmic accuracy within the Standard Model.
As main applications, I will first show how the theoretical uncertainty for the SM prediction of $V_{ud}$ based on pion $\beta$ decay is reduced by a factor of three, making it negligible even beyond the reach of future experiments. Second, I will present an evaluation of isospin-breaking corrections to $\tau \rightarrow \pi \pi \nu_{\tau}$, which are an essential ingredient for a future $\tau$-based determination of the hadronic-vacuum-polarization contribution to the anomalous magnetic moment of the muon.