Transparent conducting oxides (TCOs) play an essential role in modern optoelectronic devices through their combination of electrical conductivity and optical transparency. We review recent progress in our understanding of multi-component TCOs formed from solid-solutions of ZnO, In2O3, Ga2O3 and Al2O3, with a particular emphasis on the contributions of materials modelling, primarily based on Density Functional Theory. In particular, we highlight three major results from our work: (i) the fundamental principles governing the crystal structures of multi-component oxide structures including (In2O3)(ZnO)n, named IZO, and (In2O3)m(Ga2O3) l (ZnO)n, named IGZO; (ii) the relationship between elemental composition and optical and electrical behaviour, including valence band alignments; (iii) the high-performance of amorphous oxide semiconductors. From these advances, the challenge of the rational design of novel electroceramic materials is discussed.PACS numbers: 71.15.Mb