The last decade has witnessed important development of network softwarization that has revolutionized the practice of networks. Virtualized networks bring novel and specific requirements for the control and orchestration of containerized network functions that are scattered across the network. In this regard, the migration of virtualized network functions plays a pivotal role to best meet the requirements of optimal resource utilization, load balancing and fault tolerance. The purpose of this survey is to offer a detailed overview of the progress on container migration so as to provide a better understanding of the trade-off between the benefits associated with the migration and the practical challenges. The paper includes a classification of the placement algorithms that map the containerized network functions on the virtualized infrastructure. Following, a taxonomy of the migration techniques that perform the transfer of the containerized microservices is proposed.