Si and Ge nanowires and their heterostructure have been received widespread attention in various research fields because of the inherent advantages and the major historical roles played by these materials in contemporary microelectronics. From decades of research on two materials, integrated in-depth knowledge on the nature of material properties and manufacture process provide useful guidelines to design nanostructures and related devices with increased structural and functional complexity. In this dissertation, synthesis and applications of Ge and Si based nanowires and nanotubes in electronics, photonics, biochemical sensor, and thermoelectrics are discussed. In chapter 2, self-organizing characteristics of misfit- guided Ge quantum dots growth on Si core nanowires are systematically demonstrated. Unique Ge quantum dots growth mode caused by strain supperlattice along the Si nanowire backbone can be controlled by the choice of core diameter. Such strain-guided growth opens up a new avenue towards growth of self-organized nanoscale heterostructures. In chapter 3, fundamental study of crystalline Si nanotubes properties as a platform for electrically and biochemically functional devices is demonstrated. Four- probe current-voltage characterization of precisely probe the inherent electrical properties of crystalline Si nanotubes. Selective functionalization and loading of fluorescence dye and biomolecule inside the core of nanotubes are demonstrated lighting the potential as in- vivo drug carrier. In chapter 4, characterization of thermal transport behavior of crystalline and amorphous Si nanotubes are presented. Ultra-low thermal conductivity of crystalline nanotube below the amorphous counterpart is observed. Study on elastic properties of those nanotubes reveals new possible control mechanism of phonon transport behavior. In chapter 5, fabrication of optical polarizer by printing Ge or Ge/Si core/shell nanowires into highly compacted and ordered fashion is presented. Transmission measurement under various mechanically stressed circumstances reveals potential of nanowire polarizer as high flexible and stretchable optical filter