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Detailed information on the fission process can be inferred from the observation, modeling and theoretical understanding of prompt fission neutron and γ-ray observables. Beyond simple average quantities, the study of distributions and correlations in prompt data, e.g., multiplicity-dependent neutron and γ-ray spectra, angular distributions of the emitted particles, n-n, n-γ, and γ-γ 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 γ 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 γ 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 γ-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. The inclusion of the FREYA and CGMF codes into the MCNP6.2 and MCNPX-PoliMi transport codes, for instance, provides a new and powerful tool to simulate correlated fission events in neutron transport calculations important in nonproliferation, safeguards, nuclear energy, and defense programs. This review provides an overview of the topic, starting from theoretical considerations of the fission process, with a focus on correlated signatures. It then explores the status of experimental correlated fission data and current efforts to address some of the known shortcomings. Numerical simulations employing the FREYA and CGMF codes are compared to experimental data for a wide range of correlated fission quantities. The inclusion of those codes into the MCNP6.2 and MCNPX-PoliMi transport codes is described and discussed in the context of relevant applications. The accuracy of the model predictions and their sensitivity to model assumptions and input parameters are discussed. Finally, a series of important experimental and theoretical questions that remain unanswered are presented, suggesting a renewed effort to address these shortcomings.

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