  Quarkonium production in high-energy reactions is found to exhibit a
behaviour more universal than that expected from velocity scaling. Total rates
of quarkonia produced in hadronic interactions as well as Feynman-x and
transverse momentum distributions can be described over the full range of
accessible energies (15 < sqrt{s} < 1800 GeV) by two-stage processes. The
quarkonium production cross section factors into a process-dependent
short-distance part and a single long-distance matrix element. The first part
describing the production of a free quark--antiquark pair is the perturbatively
calculated subthreshold cross section. The non-perturbative factor turns out to
be universal, giving the model great predictive power. Furthermore we estimate
the fraction of the heavy-quark cross section leading to quarkonium for both
the charm and bottom systems. Finally, we comment on quarkonium
photoproduction.
