  We report the current understanding of heavy quarkonium production at high
transverse momentum ($p_T$) in hadronic collisions in terms of QCD
factorization. In this presentation, we highlight the role of subleading power
corrections to heavy quarkonium production, which are essential to describe the
$p_T$ spectrum of quarkonium at a relatively lower $p_T$. We also introduce
prescription to match QCD factorization to fixed-order NRQCD factorization
calculations for quarkonium production at low $p_T$.
