The concept of integrating cooperative communication in non-orthogonal multiple access (NOMA) based networks (also known as cooperative NOMA) is inspired by the need to enhance network scalability with guaranteed fair resource allocation. However, sustaining the cooperative NOMA (C-NOMA) network lifetime becomes a challenging problem due to the energy bottleneck of the devices acting as relays for weak users. To alleviate this problem, the integration of radio frequency-based energy harvesting technique known as simultaneous wireless information and power transfer (SWIPT) in C-NOMA networks has been proposed. In this article, we present an extensive review of various contributions to the performance analysis of SWIPT-aided C-NOMA networks. To begin with, we identify critical guidelines needed for efficient network design. Moreover, we present an illustration of the system model in order to understand the fundamental relationship among different network components from a technical perspective. Further to this, we categorize and present an in-depth review of notable studies based on the type of relay employed, the number of relays deployed and the type of communication protocol adopted. Finally, we identify open areas worth exploring for future research works.