This book presents the results of theoretical studies of the metal oxides γ-alumina (γ–Al2O3) and magnetite (Fe3O4) using density-functional theory (DFT) including Hubbard-U corrections for the strongly correlated Fe-3d electrons of Fe3O4 (DFT+U). Although these compounds have the same spinel structure, they present different properties, e.g., γ–Al2O3 is a typical insulator with high dielectric constant while Fe3O4 is a typical magnetic material which undergoes a metal-insulator transition. Starting from the theoretical prediction of the γ–Al2O3 structure, we have studied the (111), (001), (110) and (150) surfaces. The adsorption and dissociation of H2O onto the (111) surface is considered and H-diffusion simulated. Finally, a model for the γ–Al2O3(111)/aluminium-hydroxide interface is proposed and studied. The Fe3O4 is a metal oxide that undergoes phase a transition at TV=120 K. Applying DFT+U, we investigated the electron-phonon effects that cause a small structural distortion and lead to the insulating state with low symmetry. The Fe3O4 (001) surfaces were studied. The computed electronic and atomic structures are discussed on the light of experimental data.