Over the past two decades, grain boundary structures have been investigated, with increasing frequency, using computer simulation techniques. The accuracy of the potentials used to describe the interaction between atoms is essential to the success of any computer modelling and practically all these studies have been made assuming that the atoms exert pair-wise forces on each other. This paper discusses the applicability and limitations of this assumption and the validity and applicability of the simulation results obtained with pair-potentials. First, it is shown that certain structural features of grain boundaries are independent of the potential used. Such results form, for example, the basis of the structural unit model which relates the structures of boundaries corresponding to different misorientations. Secondly, the multiplicity of boundary structures and its physical implications are discussed. In particular, we report on the complexities of the structure of Σ=5  twist boundaries and on alternative structures of  twist boundaries near the Σ=3 twin orientation, both found by computer modelling. These results, which are of general nature, are compared with experimental observations by X-ray diffraction and transmission electron microscopy and a very good agreement is found. However, exact positions of atoms in calculated structures depend on the potential used. Hence, to study properties sensitively dependent on these positions requires to go beyond the pair-potentials.