Reliable theoretical predictions for QCD processes at collider experiments require perturbative calculations beyond leading order, which in turn demand robust methods to handle infrared singularities arising from both virtual and real radiation. In this talk, I will present the generalisation of the nested soft-collinear subtraction scheme to cope with arbitrary processes involving massless partons at hadron and lepton colliders. The scheme introduces local subtraction counter terms, benefits from a sector partition of phase space and an adaptive parametrisation of unresolved radiation, and provides a transparent physical interpretation of the integrated counter terms. I will outline
the general structure of the method, highlight key technical aspects, and discuss how these ingredients pave the way towards the automation of next-to-next-to-leading order (NNLO) QCD calculations within the subtraction scheme.
References: 2310.17598, 2503.15251, 2509.08594