As a core technology emerging from the convergence of Network Function Virtualization (NFV) and Software-Defined Networking (SDN), Service Function Chaining (SFC) enables the dynamic orchestration of Virtual Network Functions (VNFs) to support diverse service requirements. However, in dynamic network environments, SFC faces significant challenges, such as resource fluctuations, user mobility, and fault recovery. To ensure service continuity and optimize resource utilization, an efficient migration mechanism is essential. This paper presents a comprehensive review of SFC migration research, analyzing it across key dimensions including migration motivations, strategy design, optimization goals, and core challenges. Existing approaches have demonstrated promising results in both passive and active migration strategies, leveraging techniques such as reinforcement learning for dynamic scheduling and digital twins for resource prediction. Nonetheless, critical issues remain—particularly regarding service interruption control, state consistency, algorithmic complexity, and security and privacy concerns. Traditional optimization algorithms often fall short in large-scale, heterogeneous networks due to limited computational efficiency and scalability. While machine learning enhances adaptability, it encounters limitations in data dependency and real-time performance. Future research should focus on deeply integrating intelligent algorithms with cross-domain collaboration technologies, developing lightweight security mechanisms, and advancing energy-efficient solutions. Moreover, coordinated innovation in both theory and practice is crucial to addressing emerging scenarios like 6G and edge computing, ultimately paving the way for a highly reliable and intelligent network service ecosystem.