Service continuity-aware edge computing is an emerging research area that focuses on maintaining uninterrupted service delivery in highly dynamic and distributed edge environments, particularly for latency-sensitive and mission-critical applications such as autonomous vehicles, smart healthcare, industrial IoT, and immersive media. Research papers in this domain investigate strategies for seamless task migration, workload balancing, fault tolerance, and adaptive resource allocation to prevent service disruption due to node failures, network congestion, or mobility-induced changes. Studies emphasize proactive and predictive approaches, often leveraging machine learning, deep reinforcement learning, and AI-driven orchestration to anticipate workload fluctuations and optimize service continuity. Recent works also explore hybrid edge–fog–cloud architectures, blockchain-based mechanisms, and Zero Trust frameworks to enhance reliability, security, and trust in distributed environments. Multi-objective optimization approaches are commonly applied to balance service continuity with Quality of Service (QoS), Quality of Experience (QoE), energy efficiency, and operational cost. Overall, service continuity-aware edge computing research underscores the importance of designing adaptive, resilient, and intelligent frameworks capable of delivering uninterrupted, high-quality services in heterogeneous and resource-constrained edge infrastructures.