Research on Service Continuity-aware Edge Computing focuses on designing strategies and frameworks to ensure uninterrupted and reliable service delivery at the edge, despite device mobility, dynamic workloads, network variability, and resource constraints. This area addresses challenges such as real-time task migration, fault tolerance, load balancing, and seamless edge–cloud coordination to maintain continuous Quality of Service (QoS). Key research directions include predictive and adaptive task scheduling, context-aware resource allocation, and fault-tolerant service orchestration for edge nodes. Other emerging topics involve container- and microservices-based architectures for rapid service migration, energy- and latency-aware continuity strategies, and AI-driven proactive fault detection and recovery. Additionally, research on SLA-compliant edge service management, resilient multi-edge collaboration, and hybrid edge–cloud frameworks represents significant avenues for advancing reliable, efficient, and uninterrupted edge computing systems.