In the present review we summarize original results where 1) we have e
xperimentally discovered a novel class of spontaneously ordered nanost
ructures, namely equilibrium arrays of three-dimensional, coherently s
trained islands on crystal surfaces; 2) we have developed a theory of
spontaneous formation of semiconductor nanostructures in heteroepitaxi
al systems; 3) we have experimentally demonstrated the existence of a
novel class of semiconductor heterostructures, namely perfect quantum
dots having an atom-like energy spectrum; we have performed a detailed
investigation of the optical properties of quantum dots; 4) we have f
abricated quantum dot-based injection lasers demonstrating unique char
actristics, namely high-temperature stability of the threshold current
and ultra-high material gain. (C) 1998 American Institute of Physics.