The classic Madelung problem, i.e., the divergence associated with the r(-1) term in the Coulomb potential of condensed ionic systems, was cast into an absolutely convergent form that is readily evaluated by direct lattice summation, revealing a net r(-5) range of this potential. The realization that Coulomb interactions in condensed systems can actually be rather short-ranged (if the system is overall neutral) permits novel physical insights into their structure and energetics to be gained. As an example, we demonstrate that an understanding of the range and the nature of the convergence of the Coulomb potential leads naturally to the prediction, verified by computer simulations for rocksalt-structured surfaces, that all surfaces in predominantly ionic materials should be fundamentally reconstructed. The work also provides a conceptual framework for the theoretical treatment of polar surfaces and interfaces, as demonstrated for the case of the (111) stacking fault and of the (111) twin boundary in the rocksalt structure.