The necessity of data mining and knowledge discovery in database of astronomy, as well as its development in recent years, process and tasks, are reviewed. The complex characteristics of present astronomical data are analyzed, and the science requirements of data mining in astronomy are introduced. Simultaneously, the research development, hot topic and challenges in the filed of data mining and knowledge discovery in database are summarized. Its existence and development will have a prospect of wide applications in the 21st century, a great push to astronomy and also provide new challenges of knowledge and technology to astronomers. In addition, the successful applications of data mining technology in the Virtual Observatory is an important factor for its sufficient exertion.