It is now generally recognized that overlap-exchange interactions are the primary cause of the medium-dependent magnetic shielding (chemical shift) in all noble gases except helium, although the attractive electrostatic-dispersion (van der Waals) interactions play an indirect role in determining the penetration of the interacting species into the repulsive overlap-exchange region. The short-range nature of these overlap-exchange interactions, combined with the fact that they often can be approximated by simple functions of the overlap of the wave functions of the interacting species, suggests a useful semiempirical model of these chemical shifts. In it the total shielding is the sum of shieldings due to pairwise interactions of the noble gas atom with the individual atoms of the medium, with the "atomic" shielding terms either estimated by simple functions of the atomic overlap integrals averaged over their Boltzmann-weighted separations, or determined by fits to experimental data in systems whose complexity makes the former procedure impractical. Results for Xe-129 chemical shifts in the noble gases and in a variety of molecular and condensed systems, including families of n-alkanes, straight-chain alcohols, and the endohedral compounds Xe@ C-60 and Xe@ C-70 are encouraging for the applicability of the model to systems of technical and biomedical interest. (C) 2004 American Institute of Physics.