Recent data on J/psi, psi(2S), chi_c, and Upsilon production has
unraveled unexpected features of QQbar bound states production in high energy
hadronic collisions.

In the 1992-1995 runs CDF has collected large samples of J/psi, psi(2S) and
Upsilon identified through their muonic decay.  In the charmonium system all
production sources have been separately measured and compared with the
theoretical predictions.  A large excess of direct production has been
observed for both psi(2S) and J/psi.  The relative production rate for the
chi^1_c and chi^2_c has also been measured.

Results on J/psi, psi(2S) and chi_c production from the fixed target
experiments E789, E705 and E672/706 are also presented.  Important features of
the production of chramonium states are shared by fixed target and collider
data.