I review a recently introduced method for the local subtraction of infrared
divergences at next-to-next-to-leading order (NNLO) in QCD. The method aims
at minimising the complexity of the general subtraction problem through a
partition of the phase space, still allowing an analytic integration of the
ensuing subtraction counterterms. The case of final-state QCD radiation is
discussed, as well as developments concerning infrared subtraction for hadronic
collisions, relevant to LHC physics. The talk is based on hep-ph/1806.09570,
hep-ph/2010.14493.