  After a brief review of the various scenarios for quarkonium production in
ultra-relativistic nucleus-nucleus collisions we focus on the ingredients and
assumptions underlying the statistical hadronization model. We then confront
model predictions for J/$\psi$ phase space distributions with the most recent
data from the RHIC accelerator. Analysis of the rapidity dependence of the
J/$\psi$ nuclear modification factor yields first evidence for the production
of J/$\psi$ mesons at the phase boundary. We conclude with predictions for
charmonium production at the LHC.
