Abstract: With the rapid development of cloud data centers (DC), the high energy consumption has become a major problem. The physical resource in a data centers can be effectively shared to embed multiple virtual networks or virtual data centers (VDC) via virtualization. By consolidating and migrating the workloads, some idle physical machines can be shut down to improve the resource utilization and revenue, which will also reduce the energy consumption. Currently, the virtual network embedding (VNE) schemes in the data center are still challenged with problems like high complexity and real-time implementation in online mapping. Besides, multiple DC coordination based VNE is becoming increasing important as the distributed DCs will be deployed on a large scale in the future. Representative works of VNE and VDC embedding are summarized in this survey, and some key techniques and potential research and application directions are also discussed, which revolves the significance of VNE in the energy-efficient collaborative operation of distributed data centers in the future.