Edge computing enables applications to leverage computing resources near the data source to perform data processing, which can effectively cope with the explosive growth of network data. However, along with the benefits come great challenges: application developers need to explicitly manage their resources and handle the burden of scalability and load balancing; users have to pay based on the allocated resources, not the resources actually consumed; and so forth. Serverless edge computing extends the idea of serverless computing and has emerged as a compelling model for dealing with many of the challenges associated with edge infrastructure. Different from the existing works which mainly focus on the basic architectures, platforms, and optimization models, this article aims to provide a systematic and comprehensive overview of server-less edge computing networks from the perspective of networking. We first propose the network architecture and layered structure of serverless edge computing networks. Then, the communication process, as well as the implementation and deployment, is presented. Next, the promising technical challenges, including service deployment and lifecycle management, resource awareness and service discovery, service scheduling, and so on, are discussed. Finally, some potential areas for future research are highlighted.