Because of the arising requirements of emerging networks (Fifth generation and beyond) such as supporting diverse Quality of Services (QoS), low latency, and high spectral efficiency; the previous and traditional generations of communication systems are becoming inappropriate. Furthermore, due to the huge connectivity and ever-growing demands of diverse services and high data rate applications, more effective radio access techniques are required for the purpose of a full-scale implementation of the fifth generation (5G) and beyond wireless systems. Therefore; the researchers are looking for new mechanisms to accomplish these demands, and one of the key techniques been proposed is NOMA due to its capability of spectrum efficiency enhancement. In NOMA-Based systems, the information signals of various users are superimposed at the transmitter side, by utilizing the differences of channel gain to work for different users simultaneously. In this study, recent papers on resource allocation problem based on Power-Doman NOMA (PD-NOMA) in 5G networks were reviewed and the goal (objective function), optimization methods used, and obtained results of each analyzed paper are investigated. In addition, the discussed resource allocation problems were classified into: optimal rate problems and power/energy-efficient problems and the proposed solutions in each of it are analyzed. Finally, this study highlights some of the present and future challenges in this field.