GaAs-Al<sub><i>x</i></sub>Ga<sub>1–<i>x</i></sub>As (AlGaAs) core–shell nanowires show great promise for nanoscale electronic and optoelectronic devices, but the application of these nonplanar heterostructures in devices requires improved understanding and control of nanoscale alloy composition and interfaces. Multiple researchers have observed sharp emission lines of unknown origin below the AlGaAs band edge in photoluminescence (PL) spectra of core–shell nanowires; point defects, alloy composition fluctuations, and self-assembled quantum dots have been put forward as candidate structures. Here we employ laser-assisted atom probe tomography to reveal structural and compositional features that give rise to the sharp PL emission spectra. Nanoscale ellipsoidal Ga-enriched clusters resulting from random composition fluctuations are identified in the AlGaAs shell, and their compositions, size distributions, and interface characteristics are analyzed. Simulations of exciton transition energies in ellipsoidal quantum dots are used to relate the Ga nanocluster distribution with the distribution of sharp PL emission lines. We conclude that the Ga rich clusters can act as discrete emitters provided that the major diameter is ≥4 nm. Smaller clusters are under-represented in the PL spectrum, and spectral lines of larger clusters are broadened, due to quantum tunneling between clusters