Non-Orthogonal Multiple Access (NOMA) has become a promising evolution with the emergence of fifth-generation (5G) and Beyond-5G (B5G) rollouts. The potentials of NOMA are to increase the number of users, the system’s capacity, massive connectivity, and enhance the spectrum and energy efficiency in future communication scenarios. However, the practical deployment of NOMA is hindered by the inflexibility caused by the offline design paradigm and non-unified signal processing approaches of different NOMA schemes. The recent innovations and breakthroughs in deep learning (DL) methods have paved the way to adequately address these challenges. The DL-based NOMA can break these fundamental limits of conventional NOMA in several aspects, including throughput, bit-error-rate (BER), low latency, task scheduling, resource allocation, user pairing and other better performance characteristics. This article aims to provide firsthand knowledge of the prominence of NOMA and DL and surveys several DL-enabled NOMA systems. This study emphasizes Successive Interference Cancellation (SIC), Channel State Information (CSI), impulse noise (IN), channel estimation, power allocation, resource allocation, user fairness and transceiver design, and a few other parameters as key performance indicators of NOMA systems. In addition, we outline the integration of DL-based NOMA with several emerging technologies such as intelligent reflecting surfaces (IRS), mobile edge computing (MEC), simultaneous wireless and information power transfer (SWIPT), Orthogonal Frequency Division Multiplexing (OFDM), and multiple-input and multiple-output (MIMO). This study also highlights diverse, significant technical hindrances in DL-based NOMA systems. Finally, we identify some future research directions to shed light on paramount developments needed in existing systems as a probable to invigorate further contributions for DL-based NOMA system.