Quarkonia are mesons formed out of either a charm and anti-charm quark pair (charmonia, e.g. $\rm{J}/\psi$ and $\psi'$) or a beauty and anti-beauty quark pair (bottomonia, e.g. $\Upsilon$(1S), $\Upsilon$(2S) and $\Upsilon$(3S)). Their hadronic production starting very early in a heavy-ion collision, via the hard scattering of two partons, they constitute a prominent tool to study the properties of the Quark-Gluon Plasma (QGP), formed in such collisions. Two competing effects are expected to modify the quarkonium production in presence of the QGP with respect to expectations based on production rates in proton-proton (pp) collisions: a suppression due to a Debye-like color screening mechanism and an enhancement due to the (re)combination of uncorrelated heavy quark pairs from the hot medium. In absence of the QGP, quarkonium production also carry information about so-called Cold Nuclear Matter (CNM) effects, such as the modifications of the parton distribution functions in the nucleus and parton energy loss. Those are studied by measuring quarkonium production in lighter collision systems, in which the QGP is not expected to be formed. Finally, pp collisions are used not only as a mandatory near-vacuum reference for the study of hot and cold effects on quarkonia, but also to study the still debated quarkonium production mechanism as well as the possible role of Multi-Parton Interactions (MPI). In these proceedings we will present a summary of the recent results on quarkonium production presented at the International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions, and how these address the topics above.