The Internet of Ships (IoS), by integrating advanced technologies, such as the Internet of Things, cloud computing, and artificial intelligence, aims to interconnect and communicate various physical devices related to maritime transportation, including ships, ports, traffic infrastructure, and warehouses. This integration is designed to optimize transportation decision making, reduce costs, enhance efficiency, improve safety, and promote environmental sustainability. Traditional IoS adopts a cloud computing-based data processing and service model, which, due to its centralized and remotely deployed nature, often places computing nodes far from the data collection and service demand points. This setup struggles to meet the high real-time and low-latency requirements of intelligent ships, traffic organization, remote control, and other applications. Edge computing, by decentralizing computing, storage, and network resources to the edge of the IoS, enables more responsive handling of device requests. It addresses critical requirements, such as intelligent access, real-time communication, and privacy protection in the IoS environment, facilitating intelligent, green communication, efficient data processing, and timely service responses. In this article, the current state of IoS and the relevant concepts of edge computing are introduced. The edge computing enabling IoS (EC-IoS) architecture and the core technologies driving EC-IoS development are systematically discussed. Emerging applications and the case studies of EC-IoS, including intelligent ships at different autonomy levels, intelligent transportation, smart ports, and warehouses, are summarized. Finally, challenges and future opportunities in open computing environments, maritime data management, system security, and resource management are outlined, providing a reference for optimizing maritime management and autonomous navigation.