  We reconsider the complete set of four-quark operators in the Weak Effective
Theory (WET) for non-leptonic $\Delta F=1$ decays that govern $s\to d$ and
$b\to d, s$ transitions in the Standard Model (SM) and beyond, at the
Next-to-Leading Order (NLO) in QCD. We discuss cases with different numbers
$N_f$ of active flavours, intermediate threshold corrections, as well as the
issue of transformations between operator bases beyond leading order to
facilitate the matching to high-energy completions or the Standard Model
Effective Field Theory (SMEFT) at the electroweak scale. As a first step
towards a SMEFT NLO analysis of $K\to\pi\pi$ and non-leptonic $B$-meson decays,
we calculate the relevant WET Wilson coefficients including two-loop
contributions to their renormalization group running, and express them in terms
of the Wilson coefficients in a particular operator basis for which the
one-loop matching to SMEFT is already known.
