With the development of technology and its integration with scientific realities, computer systems continue to evolve as infrastructure. One of the most important obstacles in front of quantum computers with high-speed processing is that its existing systems cause security vulnerabilities. Therefore, in order to take advantage of quantum systems, existing systems that are already secure must also be secure in the post-quantum scenario. One of these systems is edge computing. There are challenges in terms of computational power for the implementation of pre- and post-quantum methods in structures with resource-constrained devices. This article reviews the post-quantum security threats of edge devices and systems and the secure methods developed for them. Although there is relatively little research in this field, it remains relevant. In the studies reviewed, lattice-based approaches are often highlighted for making edge systems quantum-resistant. Additionally, these studies indicate that there has been an increasing trend in this field in recent years. This article is categorized under: Applications of Computational Statistics > Defense and National Security Algorithms and Computational Methods > Networks and Security