Federated learning becomes increasingly attractive in the areas of wireless communications and machine learning due to its powerful learning ability and potential applications. In contrast to other machine learning techniques that require no communication resources, federated learning exploits communications between the central server and the distributed local clients to train and optimize a model. Therefore, how to efficiently assign limited communication resources to train a federated learning model becomes critical to performance optimization. On the other hand, federated learning, as a brand-new tool, can potentially enhance the intelligence of wireless networks. In this article, we provide a comprehensive overview of the relationship between federated learning and wireless communications, including basic principles of federated learning, efficient communications for training a federated learning model, and federated learning for intelligent wireless applications. We also identify some research challenges and directions at the end of this article.