  I present a brief review of the existing models for particle multiplicity
evaluation in heavy ion collisions which are at our disposal in the form of
Monte Carlo simulators. Models are classified according to the physical
mechanisms with which they try to describe the different stages of a
high-energy collision between heavy nuclei. A comparison of predictions, as
available at the beginning of year 2000, for multiplicities in central AuAu
collisions at the BNL Relativistic Heavy Ion Collider (RHIC) and PbPb
collisions at the CERN Large Hadron Collider (LHC) is provided.
