Throughout history, scientists and engineers have relied on the slow and serendipitous trial-and-error process for discovering and developing new materials. In contrast, an emerging theme in modern materials science is the notion of intelligent design of materials. Pioneered by the pharmaceutical industry and adapted for the purposes of materials science and engineering, the combinatorial approach represents a watershed in the process of accelerated discovery, development and optimization of materials. To survey large compositional landscapes rapidly, thousands of compositionally varying samples may be synthesized, processed and screened in a single experiment. Recent developments have been aided by innovative rapid characterization tools, and by advanced materials synthesis techniques such as laser molecular beam epitaxy which can be used to perform parallel-processed design and control of materials down to the atomic scale. Here we review the fast-growing field of combinatorial materials science, with an emphasis on inorganic functional materials.