Two decades ago Matsui and Satz suggested that Debye screening in the quark-gluon plasma would result in J/{psi} suppression in heavy ion collisions. Much has happened in the subsequent years, and the picture of quark-gluon plasma at present is rapidly evolving - what does it imply for the J/{psi} suppression? What are the recent RHIC and SPS results trying to tell us? What else has to be done? This talk is an attempt to address these questions.

The authors review the search for the quark-gluon plasma using the signal of the suppression of J/[psi] production in high-energy heavy-ion collisions. Recent anomalous J/[psi] suppression in high-energy Pb-Pb collisions observed by the NA50 Collaboration are examined and compared with earlier results from pA and nucleus-nucleus collisions with heavy ions of smaller mass numbers. The anomalous suppression of J/[psi] production in Pb-Pb collisions can be explained as due to the occurrence of a new phase of strong J/[psi] absorption, which sets in when the number of nucleon-nucleon collisions at a spatial point exceeds about 4 and corresponds to a local energy density of about 3.4 GeV/fm3.

The combined role of inelastic scattering with nucleons and comoving secondary particles in J/[psi] suppression is explored. An analysis of the latest FNAL and CERN data suggests that the high-density comover contribution emerges with increasing incident energy and A.