Theoretical and numerical studies of prompt fission neutrons are presented. The main results of the Los Alamos model often used in nuclear data evaluation work are reviewed briefly, and a preliminary assessment of uncertainties associated with the evaluated prompt fission neutron spectrum for n (0.5 MeV)+239Pu is discussed. Advanced modeling of prompt fission neutrons is done by Monte Carlo simulations of the evaporation process of the excited primary fission fragments. The successive emissions of neutrons are followed in the statistical formalism framework, and detailed information, beyond average quantities, can be inferred. This approach is applied to the following reactions: 252Cf(sf), nth+239Pu, n(0.5 MeV)+235U, and 236Pu(sf). A discussion on the merits and present limitations of this approach concludes this presentation.