The fundamental and technological importance of transition metal oxides, and the relationship of the present work to previous monographs dealing with transition metal oxides are reviewed. The relatively abundant 3d-transition metal oxides are contrasted with the rarer 4d- and 5d-transition metal oxides that exhibit a unique interplay between spin-orbit, exchange, crystalline electric field and Coulomb correlations. The combined effect of these fundamental interactions yields peculiar quantum states and empirical trends that markedly differ from those of their 3d counterparts. General trends in the electronic structure are related to generalized phase diagrams of the magnetic and insulating ground states. The intriguing absence of experimental evidence for predicted topological states and superconductivity in these materials are discussed.