Prior to 2010, most research on the physics and chemistry of transition metal oxides was dominated by compounds of the 3d-transition elements such as Cr, Mn, Fe, Co, Ni, and Cu. These materials exhibited novel, important phenomena that include giant magnetoresistance in manganites, as well as high-temperature superconductivity in doped La2CuO4 and related cuprates. The discovery in 1994 of an exotic superconducting state in Sr2RuO4 shifted some interest toward ruthenates. Moreover, the realization in 2008 that a novel variant of the classic Mott metal-insulator transition was at play in Sr2IrO4 provided the impetus for a burgeoning group of studies of the influence of strong spin-orbit interactions in “heavy” (4d- and 5d-) transition-element oxides. This book reviews recent experimental and theoretical evidence that the physical and structural properties of 4d- and 5d-oxides are decisively influenced by strong spin-orbit interactions that compete or collaborate with comparable Coulomb, magnetic exchange, and crystalline electric field interactions. The combined effect leads to unusual ground states and magnetic frustration that are unique to this class of materials. Novel couplings between the orbital/lattice and spin degrees of freedom, which lead to unusual types of magnetic order and other exotic phenomena, challenge current theoretical models. Of particular interest are recent investigations of iridates and ruthenates focusing on strong spin-orbit interactions that couple the lattice and spin degrees of freedom.