NNLO splitting and coefficient functions with time-like kinematics

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.