As a result of technology development, magnetic nanostructures from an object of academic examinations are transmuted into a subject of experimental analysis and become elements of electronic devices. In this talk, the term ``nanostructure" relates only to regular lattices of single-domain ferromagnetic nanogranules. Exchange interaction establishes ferromagnetic ordering of magnetic moments inside granules while the intergranule interaction is purely dipole. Granules shaped as ellipsoids of revolution or their limiting types are considered. The examples of similar systems are diversiform. Among them are regular structures of magnetic granules viewed as the medium, perspective for increasing magnetic storage density. Patterned media of that sort are usually rectangular lattices of single-domain prolate magnetic granules. Magnetic insulator nanocomposite is another example. The electrical conductivity of such a system is associated with tunnel electron transitions between granules whose probability is determined by mutual orientation of magnetic moments of the adjacent granules. The third example is a thin film of a ferromagnetic metal on a single-crystal substrate. The long-range ferromagnetic order appearing in such films is associated with the specific film growth mode: it resembles a lattice of ellipsoidal ferromagnetic granules. Ground state, magnetic phase diagram, phase transitions are studied for two and three-dimensional lattices of ferromagnetic granules with dipole intergranule interaction. Conclusions of the theory compare with results of a series of experiments.