Lattice-sum methods for computing electrostatic interactions are becoming increasingly popular in the area of molecular simulation. Although these methods are generally considered to be significantly more accurate than cutoff-based methods, there are two intrinsic difficulties linked with their application: (i) the relatively complicated mathematical formalism and somewhat non-intuitive physical picture associated with electrostatics under periodic boundary conditions makes the development of new algorithms a difficult task; (ii) the assumption of exact periodicity in simulations of liquids and solutions is an approximation and may lead to periodicity-induced artifacts, the nature and magnitude of which are still poorly characterized. The present text addresses these two issues by (i) providing a detailed and consistent derivation of the two main lattice-sum algorithms (Ewald and particle-particle–particle-mesh), and (ii) discussing the nature of periodicity-induced artifacts in the context of a few simple systems. ©2000 American Institute of Physics.