  We report on recent progress on the splitting functions for the evolution of
parton distributions and related quantities, the (lightlike) cusp anomalous
dimensions, in perturbative QCD. New results are presented for the four-loop
(next-to-next-to-next-to-leading order, N^3LO) contributions to the
flavour-singlet splitting functions and the gluon cusp anomalous dimension. We
present first results, the moments N=2 and N=3, for the five-loop (N^4LO)
non-singlet splitting functions.
