Status and Perspective of Non-perturbative Renormalization in Weak Decays

We discuss the status and the problems related to the application of the off-shell non-perturbative renormalization method in a fixed gauge to operators relevant to weak decays. In particular, we critically reappraise the method recently proposed for the $\mathrm{\Delta }I=1\mathrm{/}2$ rule. We also present a general analysis of the renormalization for the $\mathrm{\Delta }I=3\mathrm{/}2$ operators, and apply it to the $\mathrm{\Delta }S=2$ operator.