The present status of experimental and theoretical binding and transition energy determinations is reviewed. Experimental data and the most recent theoretical predictions are compared for the energies of K..cap alpha../sub 1/ X-rays, M series X-rays, K-LL Auger electrons, K, L/sub 3/, M and N levels, and the 4f spin-orbit splitting. In addition, the K..cap alpha../sub 1/ and L/sub 3/ data are fitted by Moseley-type diagrams, and data on the shallow levels and the valence bands of actinide oxides are discussed. Comparison shows that the single-particle Dirac-Fock theory and the inclusion of quantum-electrodynamic contributions predicts energies of the innermost levels generally within the accuracy of data, that is in the order of magnitude of 1 eV. However, in the N, O... shells large deviations do occur presumably due to strong many-electron interactions. The inclusion of many-electron effects in the relativistic theory remains a challenge, as do experimental investigations affording an accuracy of better than 1 eV for the various electronic levels.