This talk presents a review of recent results for quarkonium production at the LHC from ATLAS, CMS, LHCb, and ALICE. Production cross sections for $J/psi$, $psi(2S)$, and $Upsilon(mS)$, and production ratios for $chi_{c,bJ}$ are found to be in good agreement with predictions from non-relativistic QCD. In contrast, spin-alignment (polarization) measurements seem to disagree with all theoretical predictions. Some other production channels useful for investigating quarkonium hadroproduction mechanisms are also considered.