This thesis is dedicated to the growth and characterization of the optoelectronic properties of III-V semiconductor nanostructures namely nanowires and nanoscale membranes. III-V semiconductors possess promising intrinsic properties like direct band gap, high electron/- hole mobility and spin-orbit interaction which makes them interesting for a wide range of applications such as high speed electronics, optoelectronics and photovoltaics. Nanostruc- tures enable the exploitation and further functionalization of the inherent semiconductor properties. The nanostructures we study in the scope of this thesis are grown with molecular beam epitaxy which enables us to obtain ultra-pure nanostructures with high crystalline quality. In the first part of this thesis we investigate and optimize the growth of GaAs nanowires both on silicon and GaAs substrates. We employ the self-catalyzed growth technique in order to avoid the risk of foreign metal contamination. Growth on Si substrates is interesting in views of enabling the integration of existing Si microtechnology and III-V technology. GaAs nanowire growth on (111) Si substrates is achieved with self-assisted and position controlled nanowire growth techniques. In both techniques, the effects of the silicon oxide thickness and composition along with the nature of the openings are investigated. GaAs nanowires grown on (111)B GaAs substrates are employed in optomechanical and optoelectronics applications. Pristine GaAs nanowires grown on (111)B GaAs substrates are employed in scanning force microscopy thanks to asymmetric orthogonal modes they exhibit. Furthermore, GaAs/AlGaAs heterostructure nanowires demonstrate lasing when their dimensions and AlGaAs capping are optimized. The rest of this thesis is dedicated to the growth of defect-free structures. Two methods are presented to create defect-free pure zinc-blende GaAs nanostructures. The first one is to modify the polarity of GaAs nanowires. We optimize the growth parameters to obtain a high yield of (111)A nanowires on (100) GaAs. GaAs nanowires grown in (111)A direction exhibited a defect-free structure in contrast to the nanowires grown in (111)B direction. Our second approach is to grow elongated nanostructures and control their orientation to ‘lock out’ the defects. When these nanostructures, GaAs nanoscale membranes, are oriented in <11-2> direction on a (111)B GaAs substrate they exhibit pure zinc-blende crystalline structure. Their superior crystalline quality is confirmed with transmission electron microscopy and optical characterization techniques, i.e. photoluminescence and cathodoluminescence. Their growth mechanism and parameter window is investigated in detail. Next, GaAs nanoscale membranes are used as templates for quantum heterostructures. GaAs quantum wells are embedded in an AlGaAs shell around the nanoscale membranes. They are found to exhibit bright luminescence with narrow linewidth. Additionally, local alloy fluctuations in the AlGaAs shell are investigated. They exhibited sharp and localized luminescence characteristics like self-assembled quantum dots.