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 $\gamma$-ray emission from these structures in galaxy clusters and we propose a new approach to unveil their origin.\\\\\\
%
\textbf{Key words.} galaxies: clusters: general, galaxies: clusters: intracluster medium, diffuse radio emissions: radio relics, radiation mechanisms: thermal: non-thermal, acceleration of particles, gamma-rays.