This long chapter revisits and extends in differents directions and within the physical \(L^{1}\) -settings, many classical problems in spectral and scattering theory for Neutron Transport, while also exploring non-classical issues. In particular, we study neutron transport equations (with non-incoming boundary conditions) involving more complex scattering phenomena, including inelastic, downshift, and Bragg scattering, as well as space-inhomogeneous linear Boltzmann equations with power-like hard-sphere potentials. We also provide a spectral analysis for boundary conditions modeled by stochastic diffuse operators, along with a spectral gap analysis for neutron diffusion equations.