In this talk, we will introduce a rigorous approach to the study of the symmetry breaking and pattern formation phenomenon for isotropic functionals with local/nonlocal interactions in competition. More precisely, we consider a general class of nonlocal variational problems in dimension \(d\geq 1\), in which an isotropic surface term favouring pure phases competes with an isotropic nonlocal term with power law kernel favouring alternation between different phases. Close to the critical regime in which the two terms are of the same order, we give a rigorous proof of the conjectured structure of global minimizers, in the shape of domains with flat boundary (e.g. stripes or lamellae). The natural framework in which our approach is set and developed is the one of calculus of variations and geometric measure theory. This work is in collaboration with S. Daneri.