  A brief description of the IntraNuclear cascade, preequilibrium, evaporation,
fission, coalescence, and Fermi breakup models used by the last versions of our
CEM and LAQGSM event generators is presented, with a focus on our latest
development of all 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 overviewed as well. Examples of
benchmarking our models against a large variety of experimental data on
particle-particle, particle nucleus, and nucleus-nucleus reactions, involving
some very recent measurements of interest to accelerator radiation induced
activation, are discussed.
