Density functional theory (DFT) is the predominant methodology for predictive theoretical calculation of material properties used today. It is extensively applied in solid-state physics, chemistry, and materials science to model a wide range of systems on the atomic scale. The popularity of DFT is due in large part to the high-degree of accuracy provided by the methodology, coupled with a relatively low computational cost compared to alternatives like all-electron models. While DFT has been very successful at predicting diverse sets of material properties, there are crucial areas where DFT remains deficient. One of the most notable of these deficiencies is the inability of DFT to accurately describe transition metal compounds. Transition metal compounds are a huge material space with many technological applications. A comprehensive understanding of the physics underlying commonly used computational methods is required in order to best to correct these methods for a given class of compounds. This work begins with a survey of available methodologies for modelling transition metal oxides. Subsequent sections detail the properties of compounds investigated for specific technological application. Particular attention is given to high-mobility p-type semiconductors, solid-electrolytes for Li-ion batteries, and properties of amorphous phases.