Non-orthogonal multiple access (NOMA) as an efficient method of radio resource sharing has its roots in network information theory. For generations of wireless communication systems design, orthogonal multiple access schemes in the time, frequency, or code domain have been the main choices due to the limited processing capability in the transceiver hardware, as well as the modest traffic demands in both latency and connectivity. However, for the next generation radio systems, given its vision to connect everything and the much evolved hardware capability, NOMA has been identified as a promising technology to help achieve all the targets in system capacity, user connectivity, and service latency. This article provides a systematic overview of the state-of-the-art design of the NOMA transmission based on a unified transceiver design framework, the related standardization progress, and some promising use cases in future cellular networks, based on which interested researchers can get a quick start in this area.