Federated learning becomes increasingly attractive in the areas of wireless communications and machine learning due to its powerful functions and potential applications. In contrast to other machine learning tools that require no communication resources, federated learning exploits communications between the central server and the distributed local clients to train and optimize a machine learning 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 on the relationship between federated learning and wireless communications, including basic principle of federated learning, efficient communications for training a federated learning model, and federated learning for intelligent wireless applications. We also identify some future research challenges and directions at the end of this article.