Modern condensed matter physics research has produced novel materials with fundamental properties that underpin a remarkable number of cutting-edge technologies. Moreover, whoever discovers novel materials generally controls the science and technology that flows from them. It is now generally accepted that novel materials are necessary for critical advances in technologies. Transition metal oxides have recently attracted enormous interest within both the basic and applied science communities. However, for many decades, the overwhelming balance of effort was focused on the 3d-elements and their compounds; the heavier 4d- and 5d-elements (which constitute two thirds of the d-transition elements listed in the Periodic Table) and their compounds have been largely ignored until recently. We review the unusual interplay between the competing interactions present in the 4d- and 5d-transition metal oxides, and how they offer wide-ranging opportunities for the discovery of new physics and, ultimately, new device paradigms.