Interference has been a key roadblock against the effectively deployment of applications for end-users in wireless networks including fifth-generation (5G) and beyond fifth-generation (B5G) networks. Protocols and standards for various communication types have been established and utilised by the community in the last few years. However, interference remains a key challenge, preventing end-users from receiving the quality of service (QoS) expected for many 5G applications. The increased need for better data rates and more exposure to multimedia information lead to a non-orthogonal multiple access (NOMA) scheme that aims to enhance spectral efficiency and link additional applications employing successive interference cancellation and superposition coding mechanisms. Recent work suggests that the NOMA scheme performs better when combined with suitable wireless technologies specifically by incorporating antenna diversity including massive multiple-input multiple-output architecture, data rate fairness, energy efficiency, cooperative relaying, beamforming and equalization, network coding, and space-time coding. In this paper, we discuss several cooperative NOMA systems operating under the decode-and-forward and amplify-and-forward protocols. The paper provides an overview of power-domain NOMA-based cooperative communication, and also provides an outlook of future research directions of this area.