Paradigm shifts to lower-dimensional semiconductors have enabled the development of numerous electronic and photonic devices since the first fabrication of thin film quantum structures. Monolithic integrated circuits and sophisticated quantum devices, including light emitting diodes and high speed transistors, have been fabricated for the past several decades by the top-down process using thin film deposition, lithography, and etching techniques. To fabricate high-quality nanomaterials by the top-down method, heteroepitaxial thin films must be prepared prior to lithography. However, even a small lattice constant or thermal-expansion coefficient mismatch between the thin film and the substrate deteriorates the film quality by inducing the formation of many structural defects and cracks. In addition, films can be easily contaminated and damaged by lithography and etching processes. The problem in material compatibility between the film and the substrate for the top-down approach may be solved by the bottom-up method where semiconductor nanostructures are formed on the nano-scale area, offering the growth of high quality single crystal nanomaterials even on lattice-mismatched single-crystalline or amorphous substrates. Furthermore, the versatility and power of designing numerous quantum structures for electronic and optoelectronic nanodevice applications can be accomplished through one-dimensional (1-D) nanomaterial heterostructures with compositional modulations along either the axial or the radial direction. Embedding quantum structures in a single nanorod enables novel physical properties such as quantum confinement and quantum interference to be exploited. Meanwhile, position-controlled selective growth of ZnO nanorods was achieved using facet-controlled GaN micropatterns with highly anisotropic surface energies and ZnO nanowalls and nanotubes on GaN/Si substrates with a SiO2 hole pattern mask. The position-controlled vertical arrays of semiconductor nanorods offer the ideal geometry for use as functional components in nanometer-scale integrated electronics and optoelectronics on Si and glass substrates. As for the nanorod heterostructure device applications, I will demonstrate the fabrication of three-dimensional nanoarchitecture light emitting diode microarrays with quantum structures by the position-controlled growth of semiconductor nanotubes and heteroepitaxy of GaN-based quantum well layers on the nanotube arrays.