In the upcoming beyond fifth-generation (B5G), the surging demand on high network capacity and numerous access devices can hardly be satisfied by the scarce spectrum resources. Capable of sharing the same spectrum resource among multiple users, non-orthogonal multiple access (NOMA) provides an efficient method to enhance the spectrum efficiency, serving as a strong candidate for next generation multiple access (NGMA). To achieve a better performance gain of NOMA, reconfigurable intelligent surface (RIS) provides an effective leverage by reconstructing the channel conditions. Since the increasingly computational complexity and elusive communication environment in RIS-aided NOMA networks, we employ machine learning (ML) to improve network performance. In this article, we first present an overview of the NOMA, RIS, and ML. Based on the good compatibility between NOMA and RIS, we then provide a series of emerging application scenarios and associated challenges of RIS-aided NOMA. After that, we discuss the potential of ML approaches to cope with the challenges in RIS-aided NOMA. Finally, evaluation results are provided to illustrate the superiority of the RIS-aided NOMA network based on ML.