  In this talk I review the recent progress made in the calculations of
quarkonia production in fixed target experiments. NRQCD organizes the
calculations in a systematic expansion in $\alpha_s$ and $v$, the relative
velocity between the heavy quarks. Within this formalism there are octet
contributions which are not included in the color singlet model. These
contributions depend upon unknown matrix elementsof local operators which are
fit to the data. Using these fits, there are several predictions which do
indeed improve agreement with the data. However, the prediction for the
polarization of the produced states as well as the ratio of the $\chi_1$ to
$\chi_2$ cross sections differ substantially from the data for the case of pion
beams. Possible large corrections from higher twist effects are discussed as is
the issue of the the proper choice of masses.
