Abstract: With the increasing demand of edge intelligence, federated learning (FL) has been now of great concern to the industry. Compared with the traditionally centralized machine learning that is mostly based on cloud computing, FL collaboratively trains the neural network model over a large number of edge devices in a distributed way, without sending a large amount of local data to the cloud for processing, which makes the compute-extensive learning tasks sunk to the edge of the network closed to the user. Consequently, the users’ data can be trained locally to meet the needs of low latency and privacy protection. In mobile edge networks, due to the limited communication resources and computing resources, the performance of FL is subject to the integrated constraint of the available computation and communication resources during wireless networking, and also data quality in mobile device. Aiming for the applications of edge intelligence, the tough challenges for seeking high efficiency FL are analyzed here. Next, the research progresses in client selection, model training and model updating in FL are summarized. Specifically, the typical work in data unloading, model segmentation, model compression, model aggregation, gradient descent algorithm optimization and wireless resource optimization are comprehensively analyzed. Finally, the future research trends of FL in edge intelligence are prospected.