One of the primary motivations for studying nanometer-scale semiconductor crystallites, or nanocrystals, is to understand what happens when a semiconductor becomes small. This question has been studied not only for its fundamental importance, but also for its practical significance. As objects are rapidly shrinking in modern electronic and optoelectronic devices, we wish to understand their properties. To address this question, a variety of semiconductor nanocrystals have been investigated over the past two decades. Throughout these studies, one of the most important and versatile tools available to the experimentalist has been optical spectroscopy. In particular, it has allowed the description of how the electronic properties of these nanocrystals change with size. The purpose of this chapter is to review progress in this area.