Non-orthogonal multiple access (NOMA) is a promising radio access technology for the 5G wireless systems. The core of NOMA is to support multiple users in the same resource block via power or code domain multiplexing, which provides great enhancement in spectrum efficiency and connectivity. Meanwhile, with the recent advance in self-interference (SI) cancelation techniques, full duplex (FD) wireless communication has become a feasible technology enabling radios to receive and transmit simultaneously. This article aims to investigate the combination of these two emerging technologies. At first, several typical scenarios and protocols are presented to illustrate the application of FD technique in NOMA systems. Then, a novel NOMA system with FD base stations (BSs) based on centralized radio access networks (C-RAN) is proposed. Furthermore, power allocation policies are discussed for the proposed scheme, and simulation results are provided to demonstrate its superiority. Finally, challenges and research opportunities of FD NOMA systems are also identified to stimulate the future research.