Intelligent reflecting surfaces aided communication have been emerging as strong candidates to support the 6G wireless physical platforms. IRS has shown promising qualities in enhancing the spectral efficiency of wireless networks because of its capability to alter the conduct of interacting electromagnetic waves through intelligent handling of the reflections phase shifts. Also, NOMA proves itself to be superior among the other multiple access techniques as it supports a greater number of users using non-orthogonal resource allocation. This paper brings a survey over the IRS-assisted NOMA networks. The IRS and NOMA technologies, and their physical working principles are first introduced in the paper. The state-of-the-art of the IRS-assisted NOMA communication networks is next presented followed by a discussion of related performance parameters for analysis. Afterward, it discusses the resource allocation, and secrecy requirements in the IRS–NOMA networks. Furthermore, it presents the relevant work related to the optimization of energy efficiency, power efficiency and coverage. A comparison of IRS–NOMA network with MIMO–NOMA, and relay aided NOMA network is provided. Finally, a few exciting open challenges for IRS-assisted NOMA networks are identified including optimization problem using ML, identifying implementing scenarios of NOMA or OMA with IRS, PLS, and terahertz communication.