Computer modelling is at present as important method of the study of materials and their properties as experiments. Yet, experiments have been being performed for several thousands years while computer modelling started about fifty years ago. In this introductory paper we first present a historical account of the advancement of computer modelling. Since defects in crystalline materials control most of their properties but their atomic level structure and properties cannot be treated analytically, they provided the impetus for the advancement of computer modelling in materials science. In between the plethora of defects we concentrate here on dislocations since it was established via modelling that it is the non-planarity of the cores of screw dislocations in BCC metals which controls their plastic properties. This understanding than lead to the recognition that the non-planarity of dislocation cores is common in many materials and frequently determines their properties. This atomic level aspect of dislocations is considered in more details, not only for the BCC metals, and relation to the macroscopic plastic behaviour discussed. Computer modelling plays, of course, important role in studies of many other defects, such as interfaces, surfaces, irradiation induced defects etc., as well as glasses and liquids, and the last part of the paper is devoted to discussing the possible future developments, in particular from the point of view of available descriptions of atomic interactions that are the precursor of any atomistic modelling. (C) 2011 Elsevier Ltd. All rights reserved.