Abstract This article is a survey of the theoretical questions arising in the development of a convergence theory and error analysis of synthesis methods for solving neutron diffusion problems. For simplicity, we discuss convergence and the error analysis for spectral synthesis methods, in which the trial functions are functions solely of energy. The diffusion coefficient, the total and scattering cross-section data for the diffusion model are assumed spatially and energy dependent, and interior interfaces (i.e. spatial discontinuities in the diffusion coefficient and cross-section data) are present. The boundary conditions imposed are homogeneous Dirichlet conditions.