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Multi-Access Edge Computing (MEC) architectures now seem to represent the future of data processing architectures. Indeed, they have the potential to optimize the use of the backhaul network, guarantee the implementation of real-time applications and offer services adapted to the user’s context. To further improve the performance of MEC architectures, it may be worth combining them with a new technology at the physical layer: Non Orthogonal Multiple Access (NOMA). During the task offloading process, this could enhance energy efficiency, maximize the number of users benefiting from MEC services and further reduce latency. That is why the article focuses on the use of NOMA for task offloading in MEC architectures and offers a comprehensive study on the subject. First, we define a taxonomy to ensure a systematic review of existing work. We then analyze and compare existing works, classifying them according to their purpose. Based on this, we then discuss the benefits and limitations of existing work, highlighting some good practices. Finally, we identify future research directions in the field of NOMA-assisted MEC architectures.