We have studied the properties of several representative one-dimensional structures---MgO nanowires, ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ hollow nanotubes, ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ nanowires, and $\mathrm{Mg}\mathrm{O}/{\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ core/shell nanotubes---by means of first-principles-based calculations. Each of these nanostructures reveals different electronic properties with novel electronic states due to the large surface/interface of the nanocylinders. Electronic states of the ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ nanowire are localized around small clusters of atoms, and its bands appear with almost no energy dispersion. Localization is not a direct consequence of structural disorder; instead, it seems to be induced by an enhanced charge transfer due to the undercoordination on the surface. The combined effect of the $\mathrm{Mg}\mathrm{O}/{\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ nanostructure shows that the MgO is well coated and even bulk-like states can be observed. However, the magnetite suffers important atomic reconstructions losing symmetries and increasing its atomic-like behavior. Effects of axial deformations on the properties and the relation of the results to potential technological applications are discussed.