We discuss the ingredients necessary for pushing the resummation accuracy of collider observables to next-to-next-to-next-to-next-to-leading log (N4LL). We illustrate some of the techniques underlying the recent determination of these perturbative ingredients focusing both on the determination of N4LO anomalous dimensions and N3LO boundaries.
Examples will be taken both from SCET-I and SCET-II observables.