  In this talk, I start with a brief introduction to Non-Relativistic QCD
(NRQCD) and its applications to quarkonium physics. This theory has provided a
consistent framework for the physics of quarkonia, in particular, the
colour-octet Fock components predicted by NRQCD have important implications for
the phenomenology of charmonium production in experiments. We discuss the
applications of NRQCD to $J/\psi$ production at Tevatron and the tests of the
theory in other experiments. Finally we discuss the production of the ${}^1P_1$
charmonium state, $h_c$, at large-$p_T$ at the Tevatron. The observation of
$h_c$ is interesting, since its existence has yet to be experimentally
confirmed. Moreover, this rate is a $prediction$ of NRQCD, and the observation
of the $h_c$ at the Tevatron can, therefore, be used as a test of NRQCD.
