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.