Abstract: With the emergence of new network technologies such as cloud computing, software-defined network (SDN) and network function virtualization (NFV), the future network’s management is supposed to become virtual and intelligent. NFV provides an approach to realize service functions based on the virtualization technology, and it adopts general servers to substitute the dedicated middlebox in traditional network, which is able to greatly reduce the capital expenditure (CAPEX) and the operating expense (OPEX) of the telecom service provider (TSP). NFV can also improve flexibility and scalability in the management of network services. Since the end-to-end network services are usually composed of different service functions, it is an important research topic to adopt virtualization technology to build service function chain (SFC) and reasonably allocate and schedule resources. In this paper, based on the background of NFV technology, we introduce the infrastructure, technical basis, and application scenarios of SFC in the NFV enabled network. Afterward, we mainly focus on the different stages of SFC orchestration: SFC composition, SFC placement, SFC scheduling, and SFC adaptive scaling. The correlated existing theoretical research is summarized. Finally, in view of the existing problems, some solutions are proposed and the future research directions are prospected.