We review a new molecular beam epitaxy (MBE) technique we call cleaved
edge overgrowth (CEO), which makes possible fabrication of quantum wi
res or other lower dimensional quantum structures with atomic precisio
n. CEO is accomplished by performing two separate MBE overgrowths sepa
rated by an in situ cleave of the substrate sample. We review our deve
lopment of this novel method and give several examples of new structur
es recently fabricated using it.