In the traditional distributed machine learning scenario, the user’s private data is transmitted between clients and a central server, which results in significant potential privacy risks. In order to balance the issues of data privacy and joint training of models, federated learning (FL) is proposed as a particular distributed machine learning procedure with privacy protection mechanisms, which can achieve multi-party collaborative computing without revealing the original data. However, in practice, FL faces a variety of challenging communication problems. This review seeks to elucidate the relationship between these communication issues by methodically assessing the development of FL communication research from three perspectives: communication efficiency, communication environment, and communication resource allocation. Firstly, we sort out the current challenges existing in the communications of FL. Second, we have collated FL communications-related papers and described the overall development trend of the field based on their logical relationship. Ultimately, we discuss the future directions of research for communications in FL.