In the traditional distributed machine learning scenario, the user's private data is transmitted between nodes and a central server, which results in great potential privacy risks. In order to balance the issues of data privacy and joint training of models, federated learning (FL) is proposed as a special distributed machine learning with a privacy protection mechanism, which can realize multi-party collaborative computing without revealing the original data. However, in practice, FL faces many challenging communication problems. This review aims to clarify the relationship between these communication problems, and focus on systematically analyzing the research progress of FL communication work from three perspectives: communication efficiency, communication environment, and communication resource allocation. Firstly, we sort out the current challenges existing in the communications of FL. Secondly, we have compiled articles related to FL communications, and then describe the development trend of the entire field guided by the logical relationship between them. Finally, we point out the future research directions for communications in FL.