A review is given of the area of electrodeposition of materials via a mechanism of nucleation followed by diffusion controlled growth. A short historical background to the study of nucleation via potentiostatic current transient modelling is provided, followed by an outline of the major methods currently used, with some comments on their relative merits. An overview of the computer simulation of both nucleus distributions and diffusion to growing nuclei is given. Finally, methods, including optical microscopy and SPM, used for studying directly the development of surfaces on which nucleation is occurring are described. A table of some chemical systems to which the theoretical models have recently been applied is included. (C) 2003 Elsevier Science B.V. All rights reserved.