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.