After a short review of some existing models of heavy quarkonium
production in high-energy hadronic collisions,  I shall expose how it is
possible to extend the Colour Singlet Model beyond the static limit. Then,
I shall show how this extension can break gauge invariance and explain how
the latter can be restored by introducing new effective vertices. Some of
these naturally have a large contribution to the production cross section
and enable one to put the theoretical description in agreement with
experimental measurements of CDF and PHENIX.