The aim of this work has been to use atomistic computer simulation methods to calculate the thermal conductivity and investigate factors that will modify the behaviour when applied to three different oxide materials: MgO, SiO2 and SrTiO3. These were chosen as they represent distinct classes of materials and are substrates for thermoelectric devices, where one of the primary goals is to tailor the system to reduce the thermal conductivity. Chapter 1 introduces thermoelectric concepts, gives a background of the theory and a review of various important thermoelectric materials. In Chapter 2 an overview of the interatomic interactions is presented along with details on the implementation of these interactions in a simulation of a 3D periodic crystal. Chapter 3 outlines the importance of phonon processes in crystals and several approaches to the calculation of thermal conductivity are presented. MgO results are given in Chapter 4. Both the Green-Kubo and Boltzmann transport equation (BTE) methods of calculating thermal conductivity were used. The effect on thermal conductivity of two different grain boundary systems are then compared and finally extended to MgO nanostructures, thus identifying the role of surfaces and complex nanostructure architectures on thermal conductivity. In Chapter 5 two different materials with the formula unit SiO2 are considered. The two materials are quartz and silicalite which show interesting negative thermal expansion behaviour which may impact upon the thermal transport within the material. Chapter 6 presents results on the promising thermoelectric material STO. Once again the results from both Green-Kubo and BTE calculations are compared. Grain boundaries are also studied and the effect of inter-boundary distance and boundary type on the thermal conductivity is explored. Finally, a nanostructured STO system (assembled nanocubes) with promising thermoelectric applications is studied. Chapter 7 outlines the conclusions made from this work and suggests areas for future study.