The local density of states of atoms at solid surfaces can only be examined indirectly by techniques which use the core levels of the atoms as windows. The core levels themselves are measurably shifted by changes in the distribution of valence electrons. These “chemical” shifts are frequently measured by x-ray photoelectron spectroscopy (XPS), but more specific information on the local density of states is provided by techniques based on excitation by electron bombardment. Ionization spectroscopy (IS) extracts excitation edges from the total secondary emission spectrum. The threshold core level excitation probabilities can be obtained by soft x-ray characteristic isochromat spectroscopy (CIS), or more simply by soft x-ray appearance potential spectroscopy (SXAPS). Auger electron appearance potential spectroscopy (AEAPS) provides similar information. In each of these techniques the shape of the excitation edges is related to the density of conduction band states, but may be modified by final state interactions and core hole lifetime broadening. The lifetimes can be determined independently by XPS.