The bond valence theory grew out of Linus Pauling’s electrostatic valence principle, but its development was slow until crystal structure determination became sufficiently accurate to make clear how the valence of a bond correlates with its length. Armed with this quantitative link with experiment, the theory has subsequently found many uses in analysing, modelling and predicting the structures of complex crystals, surfaces and liquids. Its theorems show how the physical properties of complex materials can be understood as the consequence of their chemical structure. The theory is increasingly finding new uses in solid-state chemistry and condensed matter physics.