Zeolites are three-dimensional, crystalline silicate-based materials of interest for catalysis and separations. Computational models of zeolites must capture their three-dimensional structure, the intrinsic microscopic heterogeneity introduced by heteroatom substitutions that underlie their interesting chemical behavior, and the dynamic nature of reactive sites within the pores of molecular dimensions. In this dissertation, I will describe my use of supercell density functional theory (DFT) models for tackling these problems, focusing primarily on Brønsted acidic, Fe or Cu-exchanged chabazite (CHA) zeolites and their relationship to the catalytic chemistry of nitrogen oxides (NOx) and the partial oxidation of methane. In addition, I will also show how DFT computations are used to gain insights into the influence of extra-framework cations on zeolite property during synthesis. I will describe considerations important in model construction, applications of ab initio molecular dynamics to structure annealing and accurate computations of reaction and activation free energies, first-principles thermodynamics approaches for predicting site speciation at realistic conditions, and approaches for predicting heteroatom distributions into material models.