For the past forty years, electronic computers have grown more powerful as their basic subunit, the transistor, has shrunk. However, the laws of quantum mechanics and the limitations of fabrication techniques soon will prevent further reduction in the minimum size of today's semiconductor transistors. In order to continue this miniaturization down to the molecular scale, present-day microelectronic device designs must be replaced with new designs that take advantage of the quantum mechanical effects that dominate on such a small scale.

Semiconductor quantum dots is one of the promising material for the advanced logic devices. In this presentation, recent progress on the direct formation of GaAs/AlGaAs and InGaAs/GaAs QDs systems by Droplet Epitaxy, which has proposed and termed by us in 1990, and developed until now, are reviewed. The Droplet Epitaxy is promising for the fabrication of compound semiconductor quantum dots not only in a lattice-matched system but also in a lattice-mismatched system.