In this thesis, we have reported the MBE growth, design, and fabrication of the InGaAs quantum dots (QDs) laser/semiconductor optical amplifier, broadband QDs structure, coupled double cavity structure for terahertz emission on GaAs substrate. The emission wavelengths of the strain-induced S-K growth mode QDs structures are adjusted through the composition of QDs and strain-compensated capping layer. Also, the technique of growing high quality InGaAs QDs with solid source molecular beam epitaxy has been established and characterized by double crystal X-ray diffraction, transmission electron microscopy, photoluminescence, electroluminescence measurements. For 1.3£gm QDs laser samples, ridge waveguide lasers of the Fabry-Perot (FP) type are fabricated by wet-etching process. From the QDs laser L-I curve, the e2-hh2 transition at £f =1160nm have larger optical gain than e1-hh1 transition at £f =1220nm. The FP laser with 0.6£gm cavity length shows a lasing peak of 1160nm at threshold. As the cavity length increase to 2£gm, the lasing peak red shift to 1220nm (closed to ground state emission wavelength). This energy band gap transition phenomenon is obvious especially in the QDs laser with quantum well (QW) structure. When the injection current increase, two lasing peaks at £f= 1160 and 1175nm are observed sequentially. This unique lasing behavior is shown to be consistent with carriers localized in noninteracting dots. For the application of 1.3£gm light source, we optimum the growth condition for different needs in optical coherent tomography (OCT) light source, tandem solar cell, terahertz emission light source, etc. For the super luminescence diode (SLED) in OCT, we design multi-stacked asymmetric QDs structure (AMQD), QDs in the well structure (DWell), Dwell with p-doping in well structure to investigate the carrier recombination condition and bandwidth. Comparing with 5 structures in this study, the Dwell with p-doping in well structure has a maximum EL bandwidth exceed 198nm. The large bandwidth is attributed to the QW which increases the carrier capture rate and the p-doping which provide the efficient holes in valance band. This structure provides an excellent SLED light source solution to replace the existing program. For the tandem solar cell, we use the multi-stack QDs to compose broadband absorption in 1eV range. In order to avoid the degradation in the open circuit voltage, we use InGaAs QW to reduce the QDs strain. We observed the doping effect on the built in field through the photo-reflectance measurements. For the better photocurrent collection, we use p-doping in the QW to increase the built-in field intensity to obtain higher efficiency. For the terahertz emission, the QDs embedded in coupled double-cavity structures with an AlAs/GaAs intermediate distributed Bragg reflector (DBR) are grown on GaAs substrates. Two emission peaks at 1180, 1206 nm from the QDs corresponding to the coupled double-cavity resonant modes are observed in the high reflection band. The frequency differences for the two resonant coupled modes are of 5.5 terahertz, and have been successfully controlled by changing the pair numbers for the intermediate DBR. In addition, we have grown the InGa(Al)As nanostructures on InP substrate. The lattice constant difference between InGaAs and InP is relatively smaller compare with GaAs substrate, and it will be more challenge in epitaxial growth. After we investigate the strain, surface morphologies, optical properties for the nanostructures, we find the group III elements play an important role in the morphologies. Wire formation is attributed by the enhanced adatom diffusion length in the stepped surface front along [0-11] direction for the presence of Ga both in the nanostructure and buffer layer. Finally, we established QDs, Qwires database for the valuable new possibilities for designing new and original structures.