  A description of the IntraNuclear Cascade (INC), preequilibrium, evaporation,
fission, coalescence, and Fermi breakup models used by the latest versions of
our CEM03.03 and LAQGSM03.03 event generators is presented, with a focus on our
most recent developments of these models. The recently developed "S" and "G"
versions of our codes, that consider multifragmentation of nuclei formed after
the preequilibrium stage of reactions when their excitation energy is above 2A
MeV using the Statistical Multifragmentation Model (SMM) code by Botvina et al.
("S" stands for SMM) and the fission-like binary-decay model GEMINI by Charity
("G" stands for GEMINI), respectively, are briefly described as well. Examples
of benchmarking our models against a large variety of experimental data on
particle-particle, particle-nucleus, and nucleus-nucleus reactions are
presented. Open questions on reaction mechanisms and future necessary work are
outlined.
