The three-dimensional atom probe has been used to characterize green- and blue-emitting InxGa1-xN/GaN multiple quantum well structures with subnanometer resolution over a 100 nm field of view. The distribution of indium in InxGa1-xN samples with different compositions is analyzed. No evidence is found wherein the indium distribution deviates from that of a random alloy, which appears to preclude indium clustering as the cause of the reported carrier localization in these structures. The upper interface of each quantum well layer is shown to be rougher and more diffuse than the lower interface, and the existence of monolayer steps in the upper interfaces is revealed. These steps could effectively localize carriers at room temperature. Indium is shown to be present in the GaN barrier layers despite the absence of indium precursor flux during barrier layer growth. A strong evidence is produced to support a mechanism for the presence of indium in these layers, namely, that a layer of indium forms on the surface of the growing InxGa1-xN quantum well, and this layer then acts as a source of indium during GaN barrier layer growth.