This article focuses on the exploitation of reconfigurable intelligent surfaces (RISs) in multiuser networks employing orthogonal multiple access (OMA) or non-orthogonal multiple access (NOMA), with an emphasis on investigating the interplay between NOMA and RIS. Depending on whether the RIS reflection coefficients can be adjusted only once or multiple times during one transmission, we distinguish between static and dynamic RIS configurations. In particular, the capacity region of RISaided single-antenna NOMA networks is discussed and compared with the OMA rate region from an information-theoretic perspective, revealing that the dynamic RIS configuration is capacity-achieving. Then, the impact of the RIS deployment location on the performance of different multiple access schemes is investigated, which reveals that asymmetric and symmetric deployment strategies are preferable for NOMA and OMA, respectively. Furthermore, for RIS-aided multiple-antenna NOMA networks, three novel joint active and passive beamformer designs are proposed based on both beamformer-based and cluster-based strategies. Finally, open research problems for RIS-NOMA networks are highlighted.