The physics of Y-mesons in the hot quark-gluon plasma (QGP) is investigated in heavy-ion collisions at energies reached at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). Our model for Y suppression encompasses screening, collisional damping and gluodissociation in the QGP. It provides p_T- and centrality-dependent results for the six states involved. Most of the Y(1S)-suppression at LHC energies is found to be due to reduced feed-down, whereas the Y(2S)-suppression is mainly caused by hot-medium effects in the collectively expanding QGP. The previously predicted Y(1S)-suppression in PbPb collisions at sqrt(s_NN) = 5.02 TeV agrees with recent CMS data. At RHIC energies, comparisons with 200 GeV AuAu data from STAR are shown. In the asymmetric pPb system at sqrt(s_NN) = 8.16 TeV, both cold-matter and and hot-medium effects contribute substantially. Model comparisons with LHCb, and preliminary ALICE data are discussed.