Non-Orthogonal Multiple Access (NOMA) is a promising radio access technique for enhancing performance in next-generation cellular communications, particularly in 5G systems. Compared to Orthogonal Frequency Division Multiple Access (OFDMA), NOMA offers greater spectrum efficiency and other advantages. This paper focuses on power-domain NOMA, which uses superposition coding (SC) at the transmitter and successive interference cancellation (SIC) at the receiver. The paper surveys recent progress in NOMA for 5G systems, including capacity analysis, power allocation strategies, user fairness, and user-pairing schemes. It also discusses how NOMA integrates with other wireless communication techniques such as cooperative communications, multiple-input multiple-output (MIMO), beamforming, space-time coding, and network coding. The paper addresses implementation issues and provides avenues for future research. Key concepts covered include SC and SIC, typical NOMA schemes, and potential solutions like Cooperative NOMA (C-NOMA), fairness in NOMA, NOMA with MIMO and beamforming, coordinated systems, network NOMA, user pairing, energy efficiency, and applications in visible light communications.Non-Orthogonal Multiple Access (NOMA) is a promising radio access technique for enhancing performance in next-generation cellular communications, particularly in 5G systems. Compared to Orthogonal Frequency Division Multiple Access (OFDMA), NOMA offers greater spectrum efficiency and other advantages. This paper focuses on power-domain NOMA, which uses superposition coding (SC) at the transmitter and successive interference cancellation (SIC) at the receiver. The paper surveys recent progress in NOMA for 5G systems, including capacity analysis, power allocation strategies, user fairness, and user-pairing schemes. It also discusses how NOMA integrates with other wireless communication techniques such as cooperative communications, multiple-input multiple-output (MIMO), beamforming, space-time coding, and network coding. The paper addresses implementation issues and provides avenues for future research. Key concepts covered include SC and SIC, typical NOMA schemes, and potential solutions like Cooperative NOMA (C-NOMA), fairness in NOMA, NOMA with MIMO and beamforming, coordinated systems, network NOMA, user pairing, energy efficiency, and applications in visible light communications.