Artificial neural networks (ANNs) are recognized for their good properties in solving the non-linear classification problem. Especially, ANNs and their latest advancements in deep learning (DL) are blooming in artificial intelligence (AI) fields in the past few years. They have recently proven their abilities to handle some complex fault diagnosis problems. In the context of these backgrounds, this paper provides a concise review on the applications of ANNs to condition monitoring and fault diagnosis (CMFD) of nuclear power plants (NPPs). Firstly, a brief description of basic principle of ANNs are given. Then, a number of studies reported in both the journals and conferences are reviewed. These studies are divided into two categories according the application types of ANNs: shallow ANNs and deep ANNs. Finally, the conclusions and trends developed in the future are summarized.