Ultra-dense networks (UDNs) constitute one of the most promising techniques for supporting the 5G mobile system. By deploying more small cells in a fixed area, the average distance between users and access points can be significantly reduced; hence, dense spatial frequency reuse can be exploited. However, severe interference is the major obstacle in UDNs. Most contributions deal with the interference by relying on cooperative game theory. This article advocates the application of dense user-centric C-RAN philosophy to UDNs, thanks to the recent development of cloud computing techniques. Under dense C-RAN, centralized signal processing can be invoked for supporting CoMP transmission. We summarize the main challenges in dense user-centric C-RANs. One of the most challenging issues is the requirement of the global CSI for the sake of cooperative transmission. We investigate this requirement by only relying on partial CSI, namely, on inter-cluster large-scale CSI. Furthermore, the estimation of the intra-cluster CSI is considered, including the pilot allocation and robust transmission. Finally, we highlight several promising research directions to make the dense user-centric C-RAN become a reality, with special emphasis on the application of big data techniques.