A Review of Recent Results on Quarkonium Production at LHCb

A selection of LHCb results is presented on the production of heavy quarkonium states in $pp$ collisions, including results on $J/\psi$ and $\Upsilon$ production at $\sqrt{s}$ = 8 TeV, the measurement of prompt $J/\psi$ polarisation, the production of $\chi_{c}$ mesons from converted photons, exclusive charmonium production, double $J/\psi$ production, as well as recent results on $J\psi$ production in proton-lead collisions at $\sqrt{\rm{S_{NN}}}$ = 5 TeV.