  Quarkonium production has long been regarded as a potential signature of
deconfinement in nucleus-nucleus collisions. Recently, the production of
J/$\psi$ via regeneration within the quark-gluon plasma (QGP) or at the phase
boundary has been identified as an important ingredient for the interpretation
of quarkonium production results from lead-lead collisions at the Large Hadron
Collider (LHC). Quarkonium polarization could also be used to investigate the
properties of the hot and dense medium created at the LHC energies. In this
contribution, the latest ALICE results on quarkonium will be presented and
discussed. These include, among others, the nuclear modifications of (prompt
and non-prompt) J/$\psi$ and $\psi$(2S) production, and the J/$\psi$
polarisation, all measured with lead-lead collisions at the LHC. The results
will be compared with available theoretical model calculations.
