This article discusses some of the many-body potentials used for simulations of processes and energies in materials at the atomic scale, emphasizing their motivation and underlying physical concepts, particularly where these are not entirely empirical. The perspective is somewhat historical and describes the importance of developments of the theory of electrons in solids for the derivation of many-body (or many-atom) potential models. The models include density-dependent pairwise potentials, effective medium and embedded-atom models, and polarizable ion models. As a recent radical departure from approaches derived from the physics of electrons, the development of models based on information theory is also described.