  We present a general discussion of collider processes with not-completely
inclusive production of heavy flavors. We review the Perturbative Fragmentation
Functions formalism as the appropriate tool for studying such processes and
detail the extension of this formalism at Next-to-Next-to-Leading order. We
conclude that the prospects for the future in this field are bright and at
present are limited by the available experimental data. Hopefully, the future
ILC will be able to fill this gap.
