  We discuss recent results on the three-loop (next-to-next-to-leading order,
NNLO) time-like splitting functions of QCD and the two-loop (NNLO) coefficient
functions in one-particle inclusive e+e- annihilation. These results form the
basis for extracting fragmentation functions for light and heavy flavors with
NNLO accuracy that will be needed at the LHC and ILC. The two-loop calculations
have been performed in Mellin space based on a new method, the main features of
which we also describe briefly.
