The integration of cognitive radio (CR) technology and non-orthogonal multiple access (NOMA) techniques, referred to as CR-based NOMA system, has been recently configured as a promising solution to meet the requirements of beyond fifth generation (B5G) networks, especially those related to Internet-of-Things (IoT) applications. With such integration, power domain NOMA allows multiple users to share the same orthogonal resource blocks, while CR technology enables opportunistic bandwidth utilization by permitting secondary users (SUs) to access the licensed spectrum frequency without interrupting the primary users' (PUs) activities. To support the massive connectivity requirements of IoT-based networks, several multiple-access techniques have been recently combined with CR-based NOMA systems, including orthogonal multiple access (OMA) and multiple-antenna techniques. For example, in CR-based OMA-NOMA systems, the licensed frequency band is split into several channels, and a set of SUs is served on each channel using the NOMA technique. This paper provides an overview and analysis of the stateof-the-art CR-based NOMA network architecture. It summarizes the main design challenges related to the practical implementation of such systems. Furthermore, this paper presents the advances of combining CR-based NOMA with recent multiple-access techniques, where the potential capabilities and the design challenges of such integrated systems are also investigated and discussed. On the other hand, this paper demonstrates the potential capabilities of deploying recent technologies in CR-based NOMA networks. The technologies include intelligent reflecting surfaces, terahertz communications, machine learning, unmanned aerial vehicles, and hybrid NOMA systems. Finally, future research directions and open issues are provided and discussed. INDEX TERMS Cognitive Radio (CR), NOMA, Internet-of-Things (IoT), 5G, B5G.