We describe some recent advances in the methodology of using electronic structure calculations for materials design. The methods have been developed for the design of ordered metallic alloys and metal alloy catalysts, but the considerations we present are relevant for the atomic-scale computational design of other materials as well. A central problem is how to treat the huge number of compounds that can be envisioned by varying the concentrations and the number of the elements involved. We discuss various strategies for approaching this problem and show how one strategy has led to the computational discovery of a promising catalytic metal alloy surface with high reactivity and low cost.