Data-driven machine learning (DDML) methods for the fault diagnosis and detection (FDD) in the nuclear power plant (NPP) are of emerging interest in the recent years. However, there still lacks research on comprehensive reviewing the state-of-the-art progress on the DDML for the FDD in the NPP. In this review, the classifications, principles, and characteristics of the DDML are firstly introduced, which include the supervised learning type, unsupervised learning type, and so on. Then, the latest applications of the DDML for the FDD, which consist of the reactor system, reactor component, and reactor condition monitoring are illustrated, which can better predict the NPP behaviors. Lastly, the future development of the DDML for the FDD in the NPP is concluded.