  The status of thermal model descriptions of particle production in heavy ion
collisions is presented. We discuss the formulation of statistical models with
different implementation of the conservation laws and indicate their
applicability in heavy ion and elementary particle collisions. We analyze
experimental data on hadronic abundances obtained in ultrarelativistic heavy
ion collisions, in a very broad energy range starting from RHIC/BNL ($\sqrt
s=200$ A GeV), SPS/CERN ($\sqrt s\simeq 20$ A GeV) up to AGS/BNL ($\sqrt
s\simeq 5$ A GeV) and SIS/GSI ($\sqrt s\simeq 2$ A GeV) to test equilibration
of the fireball created in the collision. We argue that the statistical
approach provides a very satisfactory description of experimental data covering
this wide energy range. Any deviations of the model predictions from the data
are indicated. We discuss the unified description of particle chemical
freeze--out and the excitation functions of different particle species. At SPS
and RHIC energy the relation of freeze--out parameters with the QCD phase
boundary is analyzed. Furthermore, the application of the extended statistical
model to quantitative understanding of open and hidden charm hadron yields is
considered.
