Properties of excitons confined to potential fluctuations due to indium distribution in the wetting layer which accompany self-assembled InAs/GaAs quantum dots are reviewed. Spectroscopic studies are summarized including time-resolved photoluminescence and corresponding single-photon emission correlation measurements. The identification of charge states of excitons is presented which is based on results of a theoretical analysis of interactions between the involved carriers. The effect of the dots’ environment on their optical spectra is also shown.