  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. The applications of
NRQCD to $J/\psi$ production at Tevatron and the tests of the theory in other
experiments is discussed. In particular, the apparent disagreement of NRQCD
with results from HERA on inelastic photoproduction of $J/\psi$ is discussed
and it is shown that the results are rather susceptible to intrinsic transverse
momentum smearing. The photoproduction data, therefore, do not provide a good
test of NRQCD. It is argued that NRQCD may be tested stringently by looking for
the production of other charmonium resonances at the Tevatron, because the
production rates for these resonances can be predicted within the NRQCD
framework.
