Non-orthogonal multiple access (NOMA) is potentially capable of circumventing the limitations of the classic orthogonal multiple access schemes, hence it has recently received significant research attention both in industry and academia. This article is focused on exploiting multiple antenna techniques in NOMA networks, with an emphasis on investigating the rate region of multiple-input multiple-output (MIMO)-NOMA, whist reviewing two popular multiple antennas aided NOMA structures, as well as underlining resource management problems of both single-carrier and multi-carrier MIMO-NOMA networks. This article also points out several effective methods of tackling the practical implementation constraints of multiple antenna NOMA networks. Finally, some promising open research directions are provided in context of multiple antenna aided NOMA.