We review basic topics of the self-aggregation process of InAs quantum dots on the GaAs(001) surface with reference to our recent experimental and theoretical studies. Atomic-force and scanning-tunnelling microscopy, and reflection highenergy electron diffraction measurements are presented for discussing issues such as formation and composition of the wetting layer, evolution of the 2D to 3D transition, size distribution and equilibrium shape of the islands. Single-dot emission is demonstrated by micro-photoluminescence spectra of samples where quantum dots were confined on selected nanoscale areas of the surface bymolecular-beamepitaxial growth on lithographed substrates. Theoretical ab initio studies of the In diffusion on the wetting lay...