The ultra-low latency requirements of 5G/6G applications and privacy constraints call for distributed machine learning systems to be deployed at the edge. With its simple yet effective approach, federated learning (FL) is proved to be a natural solution for massive user-owned devices in edge computing with distributed and private training data. Most vanilla FL algorithms based on FedAvg follow a naive star topology, ignoring the heterogeneity and hierarchy of the volatile edge computing architectures and topologies in reality. In this paper, we conduct a comprehensive survey on the existing work of optimized FL models, frameworks, and algorithms with a focus on their network topologies. After a brief recap of FL and edge computing networks, we introduce various types of edge network topologies, along with the optimizations under the aforementioned network topologies. Lastly, we discuss the remaining challenges and future works for applying FL in topology-specific edge networks.