Physical and mechanical properties of crystalline materials are commonly controlled by the atomic structure and atomic level behaviour of crystal defects. Both experimental observations and theoretical treatments of such complex atomic scale phenomena and structures are rather limited and it is the atomic level computer modelling that is the most promising approach in such research. The principal precursor of such calculations is a reliable description of atomic interactions. Rigorous density functional theory based calculations are limited either to ideal structures or to studies of periodic arrays of very closely spaced defects, owing to the application of periodic boundary conditions and feasible block sizes. Hence, studies of large and complex systems require approximations and simplifications when describing atomic interactions but these have to reflect correctly and with sufficient accuracy the physics of bonding. In transition metals and intermetallic compounds based on these metals the bonding has a mixed nearly-free electron and covalent character. This type of bonding is well described by bond-order potentials (BOPs) that are based on the chemically intuitive tight-binding approximation to the quantum mechanical electronic structure. Apart from the quantum mechanical character, another significant advantage of BOPs is that all the calculations can be performed in real space. In this paper we first review the theoretical background of BOPs and then present the procedure for fitting BOPs using both experimental data and results of DFT-based calculations. The parameters of BOPs that have been developed for titanium, molybdenum, iridium and Ti-Al alloys, together with testing of the transferability of these potentials, are summarised in detail. In the final part we present the most representative applications of the BOPs to studies of dislocation cores and their effect on the dislocation glide. At this point we argue that these important features of the plastic behaviour relate directly to the angular character of bonding that is well represented by the BOPs. (C) 2006 Elsevier Ltd. All rights reserved.