Since virtualization technology enables the abstraction and sharing of resources with a flexible management way, the overall expenses of network deployment can be significantly reduced. Therefore, the technology has been widely applied in the core network. With the tremendous growth in mobile traffic and services, it is natural to extend virtualization technology to the cloud computing based radio access networks (CC-RANs) for achieving high spectral efficiency with low cost. In this paper, the virtualization technologies in CC-RANs are surveyed, including the system architecture, key enabling techniques, challenges, and open issues. The enabling key technologies for virtualization in CC-RANs mainly including virtual resource allocation, radio access network (RAN) slicing, mobility management, and social-awareness have been comprehensively surveyed to satisfy the isolation, customization and high-efficiency utilization of radio resources. The challenges and open issues mainly focus on virtualization levels for CC-RANs, signaling design for CC-RAN virtualization, performance analysis for CC-RAN virtualization, and network security for virtualized CC-RANs.