Combinatorial testing can use a small number of test cases to test systems while preserving fault detection ability. However, the complexity of test case generation problem for combinatorial testing is NP-complete. The efficiency and complexity of this testing method have attracted many researchers from the area of combinatorics and software engineering. This paper summarizes the research works on this topic in recent years. They include: various combinatorial test criteria, the relations between the test generation problem and other NP-complete problems, the mathematical methods for constructing test cases, the computer search techniques for test generation and fault localization techniques based on combinatorial testing.