Combinatorial Testing (CT) can detect failures triggered by interactions of parameters in the Software Under Test (SUT) with a covering array test suite generated by some sampling mechanisms. It has been an active field of research in the last twenty years. This article aims to review previous work on CT, highlights the evolution of CT, and identifies important issues, methods, and applications of CT, with the goal of supporting and directing future practice and research in this area. First, we present the basic concepts and notations of CT. Second, we classify the research on CT into the following categories: modeling for CT, test suite generation, constraints, failure diagnosis, prioritization, metric, evaluation, testing procedure and the application of CT. For each of the categories, we survey the motivation, key issues, solutions, and the current state of research. Then, we review the contribution from different research groups, and present the growing trend of CT research. Finally, we recommend directions for future CT research, including: (1) modeling for CT, (2) improving the existing test suite generation algorithm, (3) improving analysis of testing result, (4) exploring the application of CT to different levels of testing and additional types of systems, (5) conducting more empirical studies to fully understand limitations and strengths of CT, and (6) combining CT with other testing techniques.
