  The current status of various thermal and statistical descriptions of
particle production in the ultra-relativistic heavy-ion collisions experiments
is presented in detail. We discuss the formulation of various types of thermal
models of a hot and dense hadron gas (HG) and the methods incorporated in
implementing the interactions between hadrons. We first obtain the
parameterization of center-of-mass energy ($\sqrt{s_{NN}}$) in terms of
temperature ($T$) and baryon chemical potential ($\mu_B$) obtained by analyzing
the particle ratios at the freeze-out over a broad energy range from the lowest
Alternating Gradient Synchrotron (AGS) energy to the highest Relativistic
Heavy-Ion Collider (RHIC) energies. The results of various thermal models
together with the experimental results for the various ratios of yields of
produced hadrons are then compared. We have derived some new universal
conditions emerging at the chemical freeze-out of HG fireball which demonstrate
the independence with respect to the energy as well as the structure of the
nuclei used in the collision. Further, we perform the calculation of various
transport properties of HG such as shear viscosity-to-entropy density ratio
($\eta/s$) etc. using thermal model and compare with the results of other
models. We also present the calculation of the rapidity as well as transverse
mass spectra of various hadrons in the thermal HG model. The purpose of this
review article is to organize and summarize the experimental data obtained in
various experiments with heavy-ion collisions and then to examine and analyze
them using thermal models so that a firm conclusion regarding the formation of
quark-gluon plasma (QGP) can be obtained.
