This thesis is an investigation into the accuracy of hybrid density functional theory to predict the properties of two transition metal oxides: Ilmenite (FeTiO3) and haematite (sigma-Fe2O3). The hybrid density functional theory examined is Becke's B3LYP functional, which is an empirical mix of density functional theory and exact nonlocal exchange from Hartree-Fock theory. For bulk ilmenite, results from the B3LYP functional are compared with Hartree-Fock and pure density functional theory calculations. The computed properties are found to be very sensitive to the treatment of electronic exchange and correlation, with the best results being achieved using the hybrid functional. Calculations performed using the hybrid functional benefit from its better treatment of the electronic self interaction and its reasonable estimate of the pair correlation energy of the doubly occupied Fe-d orbital. To assess the performance of the hybrid functional in simulating Fe2O3 and FeTiO3 with different cation-anion coordination than that found in ilmenite or haematite, studies were performed on their high pressure polymorphs, for which there are a range of experimental results for comparison. This tests the transferability of the functional before examining cases, such as the surfaces of these materials, where there are little or no experimental or theoretical results. For the currently known high pressure polymorphs of ilmenite and haematite, the structural and elastic parameters computed using the hybrid functional are found to be in good agreement with those observed, as is the predicted stability of the phases. In ilmenite, the calculations predict the stability of a new high-pressure polymorph with space group Cmcm, occurring at pressures above 44 GPa. Calculations of the high pressure polymorphs of haematite involve the examination of a range of charge, spin, and magnetic states for each of the polymorphs. Magnetic ordering was found to be important for all the polymorphs, and for each polymorph an antiferromagnetic ordering was found to be lower in energy than the ferromagnetic ordering. The predicted transition pressure from the corundum structure and the magnetic collapse of the Fe3+ cations were in good agreement with experiment. At high pressures the lowest energy configuration for the orthorhombic perovskite structure was computed to occur with mixed high-spin /low-spin Fe3+ cations, in contrast to predictions in the literature of a Fe2+/Fe4+ solution. The CaIrO3-type structure was also computed to be stable with a mixed high-spin/ low-spin Fe3+ configuration at high pressures, and is computed to be the most stable polymorph at pressures above 46 GPa at 0 K. The structure of the ilmenite (0001) surface is examined using the B3LYP functional, and for this surface twelve different terminations are considered, with surface energies and relaxed geometries calculated. The Fe terminated (0001) surface was found to have the lowest cleavage energy, and also to be the most stable surface at low oxygen partial pressures suggesting it is most likely to form when ilmenite is cleaved under high vacuum.