The fabrication, characterization, and decoration with metallic nanoparticles of nanostructures such as nanowhiskers, nanodendrites, and fractal-like nanotrees on insulator substrates by electron-beam-induced deposition (EBID) are reviewed. Nanostructures with different morphologies of whiskers, dendrites, or trees are fabricated on insulator (Al 2 O 3 or SiO 2 ) substrates by EBID in transmission electron microscopes by controlling the irradiation conditions such as the electron beam intensity. The growth of the nanostructure is related to the accumulation of charges on the surface of a substrate during electron-beam irradiation. A high concentration of the target metallic element and nanocrystal grains of the element are contained in the fabricated nanostructures. The process of growth of the nanostructures is explained qualitatively on the basis of mechanisms in which the formation of the nanostructures is considered to be related to the nanoscaled unevenness of the charge distribution on the surface of the substrate, the movement of the charges to the convex surface of the substrate, and the accumulation of charges at the tip of the grown nanostructure. Novel composite structures of Pt nanoparticle/tungsten (W) nanodendrite or Au nanoparticle/W nanodendrite are fabricated by the decoration of W nanodendrites with metallic elements. Because they have superior features, such as a large specific surface area, a freestanding structure on substrates, a typical size of several nanometers of the tip or the branch, and high purity, the nanostructures may have applications in technologies such as catalysts, sensors, and electron emitters. However, there are still some subjects that should be further studied before their application.