  Detailed information on the fission process can be inferred from the
observation, modeling and theoretical understanding of prompt fission neutron
and $\gamma$-ray~observables. Beyond simple average quantities, the study of
distributions and correlations in prompt data, e.g., multiplicity-dependent
neutron and \gray~spectra, angular distributions of the emitted particles,
$n$-$n$, $n$-$\gamma$, and $\gamma$-$\gamma$~correlations, can place stringent
constraints on fission models and parameters that would otherwise be free to be
tuned separately to represent individual fission observables. The FREYA~and
CGMF~codes have been developed to follow the sequential emissions of prompt
neutrons and $\gamma$-rays~from the initial excited fission fragments produced
right after scission. Both codes implement Monte Carlo techniques to sample
initial fission fragment configurations in mass, charge and kinetic energy and
sample probabilities of neutron and $\gamma$~emission at each stage of the
decay. This approach naturally leads to using simple but powerful statistical
techniques to infer distributions and correlations among many observables and
model parameters. The comparison of model calculations with experimental data
provides a rich arena for testing various nuclear physics models such as those
related to the nuclear structure and level densities of neutron-rich nuclei,
the $\gamma$-ray~strength functions of dipole and quadrupole transitions, the
mechanism for dividing the excitation energy between the two nascent fragments
near scission, and the mechanisms behind the production of angular momentum in
the fragments, etc. Beyond the obvious interest from a fundamental physics
point of view, such studies are also important for addressing data needs in
various nuclear applications. (See text for full abstract.)
