Neutron-induced reactions play key roles across nuclear science answering questions from the origin of heavy elements in the Universe to cross section constraints for applications. Reactions on fission products, in particular, are relevant for astrophysical nucleosynthesis, stockpile stewardship, non-proliferation, and nuclear energy. Direct cross section measurements are not presently feasible for short-lived nuclei due to their unstable nature and current lack of a neutron target. Rather neutron-induced cross sections ((n, γ), (n,n’ γ), (n,2n), and so on) rely on statistical nuclear physics inputs and indirect experimental techniques to provide constraints. In this presentation, I will describe recent advances in statistical nuclear physics studies and indirect techniques that can provide experimentally constrained cross sections for astrophysics and applications.