Network virtualization can serve as the important technology for constructing the next-generation Internet architecture. It has been proposed as a powerful vehicle for running multiple architectures or experiments simultaneously on a shared infrastructure. It allows multiple service providers to offer customized end-to-end services over a common physical infrastructure. Virtual network embedding is a critical step for network virtualization that deals with the efficient mapping of virtual nodes and virtual links onto the substrate network resources. The virtual network-mapping problem is extremely challenging for four main practical reasons: Node and link constraints, admission control, online request, and diverse topologies. Due to different application scenarios, optimization objectives, mapping approaches, and constraints, there are many virtual network-mapping models. Unfortunately, the optimization problems of these models are generally NP-hard. The model of virtual network mapping is presented. The virtual network mapping methods and algorithms are concluded. The technological approaches to solve the optimization problems of the virtual network mapping are summarized. Finally, some open issues are presented to be further studied in the virtual network-mapping field.