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Mobile edge computing (MEC) provides a promising approach to significantly reduce network operational cost and improve quality of service (QoS) of mobile users by pushing computation resources to the network edges, and enables a scalable Internet of Things (IoT) architecture for time-sensitive applications (e-healthcare, real-time monitoring, and so on.). However, the mobility of mobile users and the limited coverage of edge servers can result in significant network performance degradation, dramatic drop in QoS, and even interruption of ongoing edge services; therefore, it is difficult to ensure service continuity. Service migration has great potential to address the issues, which decides when or where these services are migrated following user mobility and the changes of demand. In this paper, two conceptions similar to service migration, i.e., live migration for data centers and handover in cellular networks, are first discussed. Next, the cutting-edge research efforts on service migration in MEC are reviewed, and a devisal of taxonomy based on various research directions for efficient service migration is presented. Subsequently, a summary of three technologies for hosting services on edge servers, i.e., virtual machine, container, and agent, is provided. At last, open research challenges in service migration are identified and discussed.