To identify a small set of defectives from a large population of items, group testing is to group items and then test the content of the group. Group testing has been well-known for its applications in various fields including communication network, image compression, molecular biology and several computer science applications. Group testing also has strong relationships with some disciplines such as coding theory, information theory, and computational learning theory. In this lecture, I will start with a brief introduction to classical group testing and then move on to discuss two interesting group testing models: threshold group testing and interval group testing that originated from applications in chemical experiments and genome sequencing, respectively.