This article reviews developments in the understanding of x-ray-excited Auger and photoelectron spectra in the light of theoretical developments in atomic, molecular and solid-state physics. After reviewing progress in XPS and AES separately emphasis is placed on the inter-relationship between the two fields: Auger rates, for example, are the dominant contribution to core-level XPS linewidths and by combining XPS and AES it is possible to deduce information about Coster-Kronig processes which are difficult to study directly.An account is given of how the combination of measurements of environmentally dependent shifts in XPS and AES energies allows one to isolate intial-and final-state contributions which can then be related to the results of other experimental techniques.There is a brief discussion of many-electron effects which, in some instances, dominate both XPS and AES spectra.Finally we discuss how the combination of XPS and AES spectra involving valence levels enables one to study the effects of hole-state localisation.