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The understanding of quarkonium production in PbPb collisions requires the inclusion of many phenomena such as dissociation in the quark gluon plasma (QGP), partonic energy loss, statistical recombination, on top of cold nuclear matter or non-QGP effects (nuclear modifications of PDFs, initial-state energy loss, comovers). We will give an overview of recent results from the CMS Collaboration probing these different effects, using differential measurements of J/psi, psi(2S), and upsilon(1S,2S,3S) production, in pp, pPb and PbPb collisions.