Heavy quarkonia and the Quark-Gluon Plasma: a saga with (at least) three episodes

Abstract The suppression of heavy quarkonium states is considered as one of the key observables for the study of the phase transition from a system made of hadrons towards a Quark-Gluon Plasma. In the last 25 years, experiments at various facilities around the world, and in particular at Brookhaven and CERN, have studied collisions of heavy-ions looking for signals of such a transition. In this seminar, after a brief introduction, I will describe hopes, failures and successes in the study of charmonia and bottomonia and in particular of their survival in a high-temperature QCD medium. A particular emphasis will be given to very recent results obtained in this field at LHC energies by the ALICE, ATLAS and CMS experiments.