Heavy quarkonium production in hadronic collisions

Different theoretical models which attempt to describe hadronic production of heavy quarkonia are reviewed. Firstly, we consider the Color Singlet Model and point out the large discrepancies between the theoretical predictions and the results from the Tevatron detectors. Then some other models are introduced, quickly discussed and confronted with experimental results. Finally, we suggest possible ways to understand the source of the remaining discrepancies.