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Semiconductor nanostructures are used in various optoelectronic applications such as solar cells, lasers, and quantum computing. The quantum confinement within these nanostructures is realized through precise control of composition, so it is crucial to understand any compositional inhomogeneities may occur within these structures. This work focuses on compositional inhomogeneities within nanostructures for a number of III-V material systems, and how they affect their optical properties. This thesis is organized in two parts: the first part concentrates on comparing and contrasting the application of Atom Probe Tomography (APT) and Scanning Transmission Electron Microscopy (STEM) in investigating composition inhomogeneity in III-V semiconductor alloys. 2D layers, such as InGaN/GaN and GaAsBi/GaAs, and buried Quantum Dots (QDs), such as Germanium QDs in AlAs and GaSb QDs in GaAs are examined. For 2D layers, the 30 nm-thick InGaN layer only presents random alloy composition fluctuation, while QWs less than 1 nm thick show nano-clustering. For GaAsBi bulk layer, it is found that surface droplets can induce composition inhomogeneities since Ga droplets can enhance Bi incorporation. Although samples without any surface droplets are more uniform, lateral composition modulation, pores, as well as GaAsBi precipitates can occur. Surface roughness is proposed to be another cause for non-uniform Bi incorporation. Buried QD nanostructures are also studied: Ge QDs are induced by high temperature annealing and form to reduce interfacial energy. A combined APT and STEM study shows that the formation mechanism for QD depends strongly on the growth method. For instance, Droplet Epitaxy method results in the formation of smaller and more dilute GaSb QD pairs compared to the more typical Stranski-Kranstanov method. Nonetheless, both methods result in similar compositional profiles along the wetting layers. The second part discusses the role of compositional inhomogeneity and defects play in optical properties of InGaN heterostructure nanowires. For In0.4Ga0.6N/GaN nanowires, compositional inhomogeneities and defects present themselves in various aspects and affect the local optical property. A six-fold lateral branching structure is also observed, and nanowires with lateral branches are optically inactive under room temperature. Higher strained InN/In0.4Ga0.6N heterostructure nanowires have more pronounced composition induced changes. These nanowires also exhibit more complicated strain relaxation mechanisms, such as phase switching and cracking.