Combinatorial testing has rapidly gained favor among software testers in the past decade as improved algorithms have become available and practical success has been demonstrated. This chapter reviews the theory and application of this method, focusing particularly on research since 2010, with a brief background providing the rationale and development of combinatorial methods for software testing. Significant advances have occurred in algorithm performance, and the critical area of constraint representation and processing. In addition to these foundational topics, we take a look at advances in specialized areas including test suite prioritization, sequence testing, fault localization, the relationship between combinatorial testing and structural coverage, and approaches to very large testing problems.