5G is the fifth generation technology standard for cellular networks, which is already being deployed and offering many advantages for communications, such as the high degree of flexibility, the possibility of management and control of systems and resources, thus allowing to host and execute services in one or more distinct network slices, etc. Non-orthogonal multiple access (NOMA) is being considered as a key enabling technique for 5G cellular systems. The earlier generations are becoming less practical with the emergent requirements such as very high spectral efficiency, very low latency, supporting diverse quality of services (QoS). Researchers are working on different techniques to fulfill these requirements, and NOMA is one of the essentials due to its capacity to increase spectrum efficiency. NOMA schemes exploit channel gain differences to serve multiple users concurrently, by superimposing multiple users' information signals at the transmitter side. In this paper, we review, analyze and classify recent papers on resource allocation problem in 5G networks, and then we discuss the proposed solutions. In particular, the papers are classified into two main categories: power/energy-efficient and rate-optimal. For each paper, the objective, optimization method and main results are discussed.Finally, some open challenges are highlighted.