In this talk we present a new result about the compactness with respect to the H-convergence for a class of non-symmetric and nonlocal linear operators in fractional divergence form, where the oscillations of the matrices are prescribed outside the reference domain. The compactness argument presented today bypasses the failure of the classical localisation techniques, that mismatch with the nonlocal nature of the operators. In the second part of the presentation, we assume symmetry and show an equivalence between the H-convergence of the nonlocal operators and the Γ-convergence of the corresponding energies. At the end of the talk a list of some open problems and new research directions drawn from this work is presented. This research is carried out in collaboration with Maicol Caponi (University of L'Aquila) and Alessandro Carbotti (University of Salento).