Bond-order potentials are an appealing way to describe the cohesive energy of materials, because they are based on the rigourous quantum mechanics of electrons, they can be derived for semiconductors as well as transition metals, and they are suitable for large scale atomistic Simulations, yielding insights that previous, simpler models of interatomic forces could not. The concept grew out of Coulson's definition of bond orders in molecules published in 1939, and was developed into a workable scheme by David Pettifor and co-workers, starting in the 1980s. This article is an introduction to the ideas and their implementation. (C) 2006 Published by Elsevier Ltd.