In this paper, a brief overview of nanocrystallites of metal and semi-conductor materials will be presented, and then the novel synthetic method of high quality CdSe nanocrystallites developed by Bawendi group at MIT will be introduced . It will be shown that results of optical properties of surface modified nanocrystallites give the evidence that the luminescence of CdSe nanocrystallites is not originated from surface related trap states, but from intrinsic spin forbidden core states. Some of the interesting applications of CdSe nano-crystallites will also be discussed at the end.