Several methods to assess the (dis)similarity of protein structures objectively are described, some of which, when applied to non-crystallographically related protein models, are able to discriminate between significant differences and 'random noise'. Some of these methods have been used to investigate a sample of several hundred protein structures which have been solved by means of X-ray crystallography in order to investigate the extent to which non-crystallographically related protein models differ from one another. It is shown that the extent of such differences is largely dependent on the resolution of the data used for the determination and refinement of the structure and, measured by some statistics, even varies essentially linearly with the resolution. The implications of these findings for the strategies used to refine structures with non-crystallographic symmetry, in particular at low resolution, are discussed. Finally, two examples are given of recent structure determinations from this laboratory in which the presence (and employment) of non-crystallographic symmetry was crucial to the solution and refinement of the structure.