Text classification is an important research direction in the field of natural language processing. It is found that the research and analysis of text classification can help to classify and manage the information effectively and provide strong support for the application of natural language processing. The existing research has made some achievements at the theoretical and methodological level. Nevertheless, the text classification research involves many aspects such as content, domain, and technology, while the research of each subject is complicated. Therefore, there are many defects and shortcomings, which need further systematic and in-depth research. In this paper, we discuss the related theories of text categorization and Latent Dirichlet Allocation (LDA) topic model for the research of text categorization. Then, we analyze the research status of text classification for LDA topic model from three aspects:technology, method, and application. Some problems and research strategies are presented as well. Finally, future trends of text categorization are summarized.