Oxides hold great promise as new and improved materials for thermal-barrier coating applications. The rich variety of structures and compositions of the materials in this class, and the ease with which they can be doped, allow the exploration of various mechanisms for lowering thermal conductivity. In this article, we review recent progress in identifying specific oxides with low thermal conductivity from both theoretical and experimental perspectives. We explore the mechanisms of lowering thermal conductivity, such as introducing structural/chemical disorder, increasing material density, increasing the number of atoms in the primitive cell, and exploiting the structural anisotropy. We conclude that further systematic exploration of oxide crystal structures and chemistries are likely to result in even further improved thermal-barrier coatings.