Inner-shell photoionization of closed-shell systems can be described by modifications of the relativistic random-phase approximation which include relaxation effects. The inclusion of overlap integrals between orbitals of the ground state and the relaxed final state is essential. Methods are reviewed and the results of cross section and matrix element calculations on deep inner subshells are compared with experiment for several atomic systems. In some instances, polarization effects can also play a role. A technique for approximating the effects of polarization is reviewed and its application to the negative iodide ion is presented. © 2003 Published by Elsevier Ltd.