Transition metal oxides have received significant attention in recent decades due to their ability to display a wide range of novel functional properties. In particular, many oxides are able to undergo metal-to-insulator transitions as a function of external stimuli such as temperature, pressure, and electric field or through doping and defect formation. In the present dissertation, density functional theory is used to explore these phenomena in three systems: (1) the Peierls transition in NbO2, (2) defect formation necessary for HfO2’s resistive switching, and (3) La-doping of SrTiO3 and trap states that may limit conductivity. For NbO2, we use successive improvements to the exchange-correlation energy combined with experiment to improve understanding of the material’s band gap in the insulating phase and show it to be close to 1.2 eV for the direct gap with an indirect gap just below 1.0 eV. Furthermore, we are able to explain the orbital contributions to the dielectric function. Using a combination of transition state theory and phonon dispersion, we demonstrate that the phase transition is driven by a second-order structural transition of the Peierls type. For HfO2, we explore the nature of the metallic gettering layer used to create substoichiometric HfO2-x for resistive switching via an atomistic model of the hafnia-hafnium interface and use transition state theory to study the ability for oxygen to diffuse across the interface. Our investigation shows that the presence of hafnium lowers the formation energy of oxygen vacancies in hafnia, but more importantly the oxidation of hafnium through oxygen migration is energetically favored. In La-doped SrTiO3, the calculations are first used to corroborate optical and electrical measurements by giving values for the density of states effective mass as well as understanding the effect of La-doping on the conductivity and DC relaxation time. Motivated by the experimental observation that even after annealing in oxygen rich environments, heavily n-type doped SrTiO3 shows carrier concentrations inconsistent with dopant concentration, we explore the role that interstitial oxygen may play as a trapping state in SrTiO3. We find three meta-stable sites and that for n-type SrTiO3, interstitials with mid-gap states are favored.