This book is devoted to the study of a few typical nanostructures and arrays of nanostructures that are expected to find many applications, such as metamaterials. Beginning with a brief discussion on a general historical perspective of this new emergent field, new methods to deal with it, such as the available numerical methods, the principle of biomimetic applications, and the powerful field of artificial intelligence, the book covers a variety of topics, including semiconductors, magnetic materials of different components, of different structures, and of different arrangements, and new chemical compounds based on which the results of different numerical simulations and experimental observations are compared. Several significant results have also been presented. For instance, the computation of the magneto-elastic behavior of a core-shell nanostructure involving spin crossover transitions paves the way to numerous extensions in three dimensions and of course to applications.