In recent years, non-local operators have attracted considerable attention in the calculus of variations, motivated by some works by Braides and Dal Maso. In this thesis, after illustrating the necessary preliminary tools, we review the main results concerning Γ-convergence and integral representability of such functionals. Within this setting, we then focus our study on the homogenization of a class of non-local functionals featuring a rapidly oscillating periodic weight. By means of two-scale convergence, we explicitly evaluate the Γ-limit for constant target functions and show how the interaction between periodicity and non-locality induces the formation of highly oscillatory minimizing sequences. Finally, drawing on a recent counterexample by Braides, we prove that the resulting effective functional cannot be represented through a standard double-integral formulation, highlighting the failure of integral representability in this homogenization regime..