An ab initio approach is delineated for obtaining X-ray absorption spectra as provided by many-body perturbation theory, together with its realization within an all-electron framework. Employing the Bethe–Salpeter equation, excitations from different absorption edges in a broad range of material classes are addressed, analysing exciton binding strengths and character. Situations in which the supercell core-hole approach is likely to fail are also discussed.