Take a stable-driven SDE dXt = b(t,Xt)dt + dZt (E), where b is a singular drift (Hölder, Lebesgue or distributional). In this talk, I will introduce an Euler discretization of (E) and the metrics used to study its convergence. I will then discuss how we can forego the usual regularity assumptions on b by relying instead on the regularity of the law of (E) and on estimates of this law in the dual space of b, as well as the associated results for the weak error. I will also present a few unpolished ideas on how one might try to improve on those techniques. This talk is based on joint works with Stéphane Menozzi and Benjamin Jourdain (https://hal.science/hal-04571879 and https://hal.science/hal-04733240)