This article describes the usefulness of embedded cluster and periodic models to solve a number of problems in computational materials science. To this end, two different well-defined problems are selected and discussed. The first problem concerns magnetic coupling in high Tc superconductor parent compounds. It is taken to exemplify the application of quantum chemical methods to derive excited-state properties of extended systems. The second problem concerns the selectivity of a partial oxidation reaction catalyzed by a metal surface. This second example serves to illustrate the efficacy of solid-state band theory methods in the study of chemical reactions taking place at surfaces. Possible extensions of ab initio computational materials science are further discussed.