In the 1992-195 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_c^1 and chi_c^2 has also been measured.  The unexpected results have lead
to a profound revisitation of the theory of the production of QQ-bar bound
states in high energy hadronic collisions.