Non-orthogonal multiple access (NOMA) becomes a key technology in 5G as it can improve the spectral efficiency in cellular systems by exploiting the power difference between users. In this talk, we review the principles of NOMA and discuss existing approaches as well as new results. In particular, we present optimization problems for resource allocation in downlink NOMA under various conditions and discuss NOMA based random access that can be used for uplink NOMA to support massive connectivity which is vital for machine-type communications in 5G.