Massive multiple-input multiple-output (MIMO) and non-orthogonal multiple access (NOMA) are two key techniques for enabling massive connectivity in future wireless networks. A massive MIMO-NOMA system can deliver remarkable spectral improvements and reduced communication latency. Nevertheless, the uncontrollable stochastic behavior of the wireless channels can still degrade its performance. In this context, intelligent reflecting surface (IRS) has arisen as a promising technology for smartly overcoming the harmful effects of the wireless environment. The disruptive IRS concept of controlling the propagation channels via software can provide attractive performance gains to the communication networks, including higher data rates, improved user fairness, and, possibly, higher energy efficiency. In this article, in contrast to the existing literature, we demonstrate the main roles of IRSs in MIMO-NOMA systems. Specifically, we identify and perform a comprehensive discussion of the main performance gains that can be achieved in IRS-assisted massive MIMO-NOMA (IRS-NOMA) networks. We outline exciting futuristic use case scenarios for IRS-NOMA and expose the main related challenges and future research directions. Furthermore, throughout the article, we support our in-depth discussions with representative numerical results.