  We study the evolution of charmonia as they collide with the constituents of
the fireball produced in high-energy nucleus-nucleus collisions. The latter
evolves in a manner controlled by the equation of state as given by lattice
QCD, and is constructed in such a way that the observed hadronic spectra are
correctly reproduced. A kinetic description of charmonium interactions with
both quark-gluon and hadronic degrees of freedom allows to study in detail the
evolution in different regimes, controlled by collision energy, kinematics and
geometry. The data collected at the CERN-SPS accelerator are well described and
new estimates for J/psi production at BNL-RHIC are presented.
