Non-orthogonal multiple access techniques have been proposed recently for 5G wireless systems and beyond to improve access efficiency by allowing many users to share the same spectrum. Due to the strong co-channel interference among mobile users introduced by NOMA, it poses significant challenges for system design and resource management. This article reviews resource management issues in NOMA systems. The main taxonomy of NOMA is presented by focusing on the two main categories of resource reuse: power-domain and code-domain NOMA. Then a novel radio resource management framework is proposed based on game-theoretic models for uplink and downlink transmissions. Finally, potential applications and open research directions in the area of resource management for NOMA are provided.