This article presents advances in resource allocation for downlink non-orthogonal multiple access (NOMA) systems, focusing on user pairing and power allocation algorithms. The former pairs the users to obtain high capacity gain by exploiting the channel gain difference between the users, while the latter allocates power to users in each cluster to balance system throughput and user fairness. Additionally, the article introduces the concept of cluster fairness and proposes the divide-and-next-largest-difference-based user pairing algorithm to distribute the capacity gain among the NOMA clusters in a controlled manner. Furthermore, performance comparison between multiple-input multiple-output NOMA (MIMO-NOMA) and MIMO orthogonal multiple access (MIMO-OMA) is conducted when users have pre-defined quality of service. Simulation results are presented, which validate the advantages of NOMA over OMA. Finally, the article provides avenues for further research on resource allocation for downlink NOMA.