Highly luminescent nanostructures, particularly highly luminescent quantum dots, are provided. The nanostructures have high photoluminescence quantum yields and in certain embodiments emit light at particular wavelengths and have a narrow size distribution. The nanostructures can comprise ligands, including C5-C8 carboxylic acid ligands employed during shell formation and/or dicarboxylic or polycarboxylic acid ligands provided after synthesis. Processes for producing such highly luminescent nanostructures are also provided, including methods for enriching nanostructure cores with indium and techniques for shell synthesis.