The edge computing paradigm is becoming increasingly commercialized due to the widespread adoption of wireless communication technologies and the growing demand for compute-intensive mobile applications. Edge computing complements the cloud computing model by deploying computation, storage, and network resources to the edge locations of wireless access networks, empowering end devices to run resource-intensive applications. In order to promote the commercialization of edge computing, it is important to explore effective ways to reduce the cost of edge computing networks. This paper provides a comprehensive review of the research findings in recent years, offering a clear perspective on the research dynamics. This paper first recalls the architectural framework of edge computing. Then, the main optimization objectives and optimization methods are comprehensively described. Mainstream mathematical models for cost reduction are then shown in depth. The paper also discusses the methods used to evaluate the effectiveness. Then, typical examples of typical application scenarios for edge computing networks are examined in depth. Finally, the paper identifies some unresolved issues. We expect future research to make more attempts in these directions.