Combinatorial testing is a method that can reduce cost and improve test effectiveness significantly for many applications. The key insight underlying this form of testing is that not every parameter contributes to every failure, and empirical data suggest that nearly all software failures are caused by interactions between relatively few parameters. This finding has important implications for testing because it suggests that testing combinations of parameters can provide highly effective fault detection. This article introduces combinatorial testing and how it evolved from statistical Design of Experiments approaches,explains its mathematical basis, where this approach can be used in software testing, and measurements of combinatorial coverage for existing test data.