Radio relics are diffuse radio sources which are detected usually at the outskirts of galaxy clusters. They provide important information about the origin of non-thermal processes taking place in the cluster atmospheres. At the time of writing this paper, 78 relics are known, while currently available models predict that a much larger number of these sources should exist. We discuss in this paper the constraints on the combined radio and γ-ray emission from these structures in galaxy clusters and we propose a new approach to unveil their origin.