Nanocrystals of metals, oxides and semiconductors have been studied intensely in the last several years by different chemical and physical methods. In the past decade the realization that the electronic, optical, magnetic and chemical properties of nanocrystals depend on their size has motivated intense research in this area. This interest has resulted in better understanding of the phenomena of quantum confinement, mature synthetic schemes and fabrication of exploratory nanoelectronic devices. The past couple of years has seen heightened activity in this area, driven by advances such as the ability to synthesize nanocrystals of different shapes. In this chapter, we review the progress in the area in the above period with emphasis on growth of semiconductor nanocrystals. Illustrative examples of the advances are provided. Several reviews have appeared in this period, seeking to summarize past as well as current wo