The research described in this dissertation involved the use of transmission electron microscopy (TEM) to characterize II-VI and III-V compound semiconductor quantum dots (QDs) and dilute-nitride alloys grown by molecular beam epitaxy (MBE) and intended for photovoltaic applications. The morphology of CdTe QDs prepared by the post-annealing MBE method were characterized by various microscopy techniques including high-resolution transmission electron microscopy (HR-TEM), and high-angle annular-dark-field scanning transmission electron microscopy (HAADF-STEM). Extensive observations revealed that the of QD shapes were not well-defined, and the QD size and spatial distribution were not determined by the amount of CdTe deposition. These results indicated that the formation of II-VI QDs using a post-annealing treatment did not follow the conventional growth mechanism for III-V and IV-IV materials. The structural properties of dilute-nitride GaAsNx films grown using plasma-assisted MBE were characterized by TEM and HAADF-STEM. A significant amount of the nitrogen incorporated into the dilute nitride films was found to be interstitial, and that fluctuations in local nitrogen composition also occurred during growth. Post-growth partial relaxation of strain resulted in the formation of {110}-oriented microcracks in the sample with the largest substitutional nitrogen composition. Single- and multi-layered InAs QDs grown on GaAsSb/GaAs composite substrates were investigated using HR-TEM and HAADF-STEM. Correlation between the structural and optoelectronic properties revealed that the GaAsSb barrier layers had played an important role in tuning the energy-band alignments but without affecting the overall structural morphology. However, according to both XRD measurement and electron microscopy the densities of dislocations increased as the number of QD layers built up. An investigation of near-wetting layer-free InAs QDs incorporated with AlAs/GaAs spacer layers was carried out. The microscopy observations revealed that both embedded and non-embedded near-wetting layer-free InAs QDs did not have well-defined shapes unlike conventional InAs QDs. According to AFM analysis and plan-view TEM characterization, the InAs QDs incorporated with spacer layers had smaller dot density and more symmetrical larger sizes with an apparent bimodal size distribution (two distinct families of large and small dots) in comparison with conventional InAs QDs grown without any spacer layer.