The recently demonstrated ability to measure double-hole core-ionization energies in first-row elements has led to a renewed interest in the use of such energies to investigate the effects of initial-state charge distribution and final-state charge rearrangement on the energies of chemical processes that involve addition of charge to a molecule. With theoretical calculations for the molecules CH4-nXn, X = F, Cl, and for C(CH3)(4) as a basis, the relationships between one-hole and two-hole ionization energies, on one hand, and initial-state and final-state effects, on the other, are reviewed. It is shown that higher-order corrections to the traditionally used relationships are quantitatively significant but do not lead to qualitatively different conclusions. The role of the Wagner plot as a way to display the relationships among the various quantities of interest is discussed, and a generalized Wagner plot for displaying two-site double-hole ionization energies is presented. Some possible applications of measurements of double-hole ionization energies to the investigation of molecular conformation and molecular fragmentation are discussed.