Towards an understanding of the production mechanism of heavy quarkonia

Heavy quarkonium is a multi-scale system, which covers both perturbative and nonperturbative regimes of QCD. Study of heavy quarkonium production can provide useful information for the hadronization and the formation of QCD bound states. However, nearly 40 years after the discover of J/\psi in 1974, the production mechanism of heavy quarkonium is still not well understood. The widely accepted theory at present is the Non-Relativistic QCD (NRQCD) factorization, which, unfortunately, suffers from many difficulties. In this talk, I will review the current status of studies regard production mechanism and highlight plentiful progresses in recent years. I will also discuss possible solutions for the difficulties in NRQCD factorization.