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The atomistic modelling of materials with effective model potentials requires a reliable description of the breaking and making of interatomic bonds in different atomic environments. The bond-order potentials provide such a transferable description of atomic bonding while at the same time they are computationally efficient for application in largescale atomistic simulations. We give an overview of the fundamentals of bond-order potentials and their derivation from the tight-binding electronic structure by linking the atomic structure to the electronic structure. We discuss the application of the structural energy difference theorem for studying trends in crystal phase stability and provide a brief summary of representative examples for modelling metals, hydrocarbons, and semiconductors with analytic and numerical bond-order potentials.