Theoretical issues in J/ψ suppression

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.