Three and four-body intervortex forces in the Ginzburg-Landau models of single- and multicomponent superconductivity

► Non-pairwise, three-body, vortex interactions in type-1, type-2 and type-1.5 superconductors. ► Lack of vortex interactions in Bogomol'nyi limit. ► Non-pairwise, four-body, vortex interactions in type-1, type-2 and type-1.5 superconductors.