Significant developments have occurred in the area of III-V compound semiconductor nanostructures. The scope of developments includes quantum dots and nanowires epitaxially grown on Si substrates, as well as their applications in light emitting diodes and lasers. Such nanoscale heterostructures exhibit remarkable structural, electrical, and optical properties. The highly effective lateral stress relaxation, due to the presence of facet edges and free surfaces, enables the achievement of nearly defect-free III-V nanoscale heterostructures directly on Si, in spite of the large lattice mismatches and the surface incompatibility. With the incorporation of multiple quantum dot layers as highly effective three-dimensional dislocation filters, self-organized quantum dot lasers monolithically grown on Si exhibit, for the first time, relatively low threshold current (Jth = 900 A/cm2) and very high temperature stability (T0 = 244 K). III-V semiconductor nanowire light emitting diodes on Si, with emission wavelengths from UV to near-infrared, have also been demonstrated.