In theory all the information regarding the three dimensional structure of a liquid is contained in the pair distribution functiong(r)or, equivalently, the structure factorA(Q), for a system with purely pairwise additive potentials. RMC is a method for modelling the structures of disordered systems based on the experimentally measured structure factor(s). We have performed some theoretical tests of the method, using input data calculated from simulations for various systems, which show that RMC does indeed work successfully if the potentials are pairwise additive. In cases where they are not then the imposition of constraints, e.g. modelling molecular systems with molecules rather than atoms, can enable the three dimensional structure to be determined. When the potentials are very complex, which usually makes the problem unsuitable for MC or MD simulations, RMC with constraints is still a valuable way of distinguishing between various structural possibilities.