Ternary InGaN and AlGaN alloys have been sought after for the application of various optoelectronic devices spanning a large spectral range between the deep ultraviolet and infrared, including light-emitting diodes, and laser diodes. Their non-ideal alloy mixing, and differences in bond energy and in adatom diffusion are established as the cause for various types of nanoscale compositional inhomogeneity commonly observed in nitride thin films. Growth in a nanowire geometry can overcome the phase separation, surface segregation, and chemical ordering by providing enhanced strain relaxation of the large lattice mismatch at the free surfaces. In this dissertation, the spectral and spatial luminescence distributions of ternary III-N alloy nanowire heterostructures are investigated and correlated to structural and chemical properties with scanning transmission electron microscopy. Quantitative elemental mapping of InGaN/GaN dot-in-a-wire structures using electron energy-loss spectroscopy revealed compositional non-uniformity between successive quantum dots. Local strain mapping of the heterostructure showed a dependence of the incorporation of indium on the magnitude of the out-of-plane compressive strain within the underlying GaN barrier layer. Cathodoluminescence spectroscopy on individual nanowires presented diverse emission properties, nevertheless, the In-content variability could be directly correlated to the broad range of peak emission energies. Atomic-level chemical ordering within the InGaN was then reported, and attributed to the faceted growth surface in nanowires that promotes preferential site incorporation by In-atoms that allows for better strain relaxation. Distinct atomic-scale alloy inhomogeneities were also investigated in AlGaN nanowires, which evidenced spatial localization of carriers taking place at the resulting energy band fluctuations. A high spectral density of narrow emission lines arose from such compositional modulations, whose luminescence behaviours exhibit a dependence on the nature of the compositional fluctuations from which they originate. / Thesis / Doctor of Philosophy (PhD)