Semiconductor nanocrystals are a system which has been the focus of interest due to their size dependent properties and their possible use in technological applications. Many chemical and physical properties vary systematically with the size of the nanocrystal and thus their study enables the investigation of scaling laws. Due to the increasing surface to volume ratio as size is decreased, the surfaces of nanocrystals are expected to have a large influence on their electronic, thermodynamic, and chemical behavior. In spite of their importance, nanocrystal surfaces are still relatively uncharacterized in terms of their structure, electronic properties, bonding, and reactivity. Investigation of nanocrystal surfaces is currently limited by what techniques to use, and which methods are suitable for nanocrystals is still being determined. This work presents experiments using x-ray and electronic spectroscopies to explore the structure, reactivity, and electronic properties of semiconductor (CdSe, InAs) nanocrystals and how they vary with size. Specifically, x-ray absorption near edge spectroscopy (XANES) in conjunction with multiple scattering simulations affords information about the structural disorder present at the surface of the nanocrystal. X-ray photoelectron spectroscopy (XPS) and ultra-violet photoelectron spectroscopy (UPS) probe the electronic structure in terms of hole screening, and also give information about band lineups when the nanocrystal is placed in electric contact with a substrate. XPS of the core levels of the nanocrystal as a function of photo-oxidation time yields kinetic data on the oxidation reaction occurring at the surface of the nanocrystal.