Abstract. In this talk, I will explain the elastic interactions in the dark sector which are described phenomenologically by a momentum transfer coupling, modifying only the linear and non-linear cosmological perturbations but not the background cosmology. I will show how non-altering background interactions can have measurable imprints in observables like the matter power spectrum or how they can alleviate the σ_8 tension, and the possible effects on the bias or on the relative velocity of matter components. Finally, I will explain how those couplings can alter the non-linear process of formation of structures.