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The physics of the innermost shells of atoms is qualitatively different in several respect from that of outer electrons. For single deep holes, correlation effects are slight, while the effects of relativity are pronounced and quantum-electrodynamic shifts can be substantial. These relativistic and QED effects can be explored with high precision because many-body aspects are limited and selfconsistent-field approaches can be relied upon. Problems of particular current interest concern the screening of the self energy and the effect of the Breit interaction on multiplet splitting and on x-ray hypersatellite shifts. Experimental studies as well as calculations of the properties of few-hole and few-electron atomic systems can lead to significant tests of current theory.