Recent Progress on Perturbative QCD Fragmentation Functions

The recent development of perturbative QCD (PQCD) fragmentation functions has strong impact on quarkonium production. I shall summarize $B_c$ meson production based on these PQCD fragmentation functions, as well as, the highlights of some recent activities on applying these PQCD fragmentation functions to explain anomalous $J\mathrm{/}\psi$ and ${\psi }^{\mathrm{\prime }}$ production at the Tevatron. Finally, I discuss a fragmentation model based on the PQCD fragmentation functions for heavy quarks fragmenting into heavy-light mesons.