First-principles calculations based on density functional theory are an invaluable tool in the prediction and understanding of materials properties based on their atomic and electronic structure. Computational results provide relevant insight for applications in the energy sector and in novel computational platforms. We begin by addressing a longstanding problem: the computation of binding energies and hyperfine interactions for shallow dopants in semiconductors. We have developed new techniques for calculating these properties with remarkable accuracy, providing guidance for engineering of spin qubits. We move on to electronic complex oxides, studying electron-electron scattering in SrTiO3. We develop a general methodology to calculate electron-electron scattering rates, and identify the conditions under which the mechanism gives rise to a well-known T2 power law in resistivity. We then turn to the unconventional electronic phase found in the spin-orbit Mott insulator Sr3Ir2O7. The electron-doping-driven metal-insulator transition is studied and structural distortions in the correlated metallic state are shown to arise from a different mechanism from the transition itself. Turning finally from electronic conduction to ionic conduction, we study hydrogen transport and optical properties in BaCeO3. We establish a new understanding of electron localization in this material and explain the results of luminescence experiments. In SrCeO3, cation vacancies are shown to be an important source of proton traps which impede diffusion, and known benefits of doping are explained as resulting from a suppression of these vacancies. In each material, advances in fundamental understanding guide experiment and advance applications.