High energy heavy ion collisions are expected to produce hadron densities far beyond the density in nuclei,?0 = 0.16 fm−3. Remarkably, no single measurement from the AGS and SPS light ion programs with projectiles A ≤ 32 stands out as unambiguous evidence of these extreme densities. To separate the high density signals from the background effects that result, e.g. from scattering with primary nucleons, careful systematic studies of hadron-nucleus, hA, and nucleus-nucleus, AB, data are needed. In this talk the author surveys the ongoing systematic study of the most notorious case in point -- J/? suppression. In principle, measurements of J/? suppression provide a probe of the densities obtained in AB collisions that is also sensitive to quark gluon plasma production. The latest results from SPS experiment NA38 reported by A. Romana in these proceedings show that the ratio of cross sections in the dimuon channel B{sub??}?{sub {psi}}/?{sub cont} is reduced by a factor 0.50 ± 0.05 in central S+U compared to minimum bias pU collisions at 200 AGeV. This is precisely the sort of suppression that one expects if high densities are obtained. On the other hand, a target-mass dependence suggestive of this suppression is found in hA collisions where high densities are not expected. At 200 GeV, NA38 finds that B{sub {mu}{mu}}?{sub {psi}}/?{sub cont} falls to 0.84 ± 0.08 in pU compared to pCu. The hA suppression in this kinematic regime is likely due to a combination of nuclear effects: nucleon absorption and shadowing.

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.

The J/[psi] suppression was originally proposed as a signature of the quark-gluon plasma. Strong suppression of J/[psi] production was indeed observed recently by the NA50 Collaboration at CERN SPS. Is it the first signature of a long-awaited quark-gluon matter, or just a peculiar combination of ''conventional'' effects acting together to produce the puzzling pattern observed experimentally? In this lecture, I am trying to summarize the existing theoretical explanations.

The anomalous suppression of J/[psi] production in Pb-Pb collisions at 158 GeV observed by the NA50 Collaboration can be explained as due to the occurrence of a new phase of strong J/[psi] absorption, which sets in when the local energy density exceeds about 3.4 GeV/fm[sup 3]. The peculiar behavior of the[psi][sup']/[psi] ratio in[ital p]-A and nucleus-nucleus collisions can be understood as due to approximately equal[psi]-N and[psi][sup']-N absorption cross sections, but greater absorption cross sections for[psi][sup'] than J/[psi] with regard to absorption by soft particles and matter in the new phase.