Using the modified embedded atom model in conjunction with a self-consistent tight-binding method, we investigated the lowest-energy structures of Fe monolayers and isolated Fen clusters (n = 2-19) supported on the Ni(111) surface. In keeping with experimental findings, our calculations predict that the atoms of the monolayer occupy face-centred cubic (fcc) rather than hexagonal close-packed (hcp) sites. Likewise in agreement with experiment we found that Fe layers stack with a pseudomorphic fcc structure up to two monolayers, beyond which they stack as bcc(110). The structures of supported Fe clusters are predicted to be two-dimensional islands maximizing the number of nearest-neighbour bonds among the adsorbed Fe atoms, and their average magnetic moments per atom decrease towards that of the supported Fe monolayer almost monotonically as n increases. Finally, a pair of Fe3 clusters on Ni(111) were found to exhibit virtually no interaction with each other even when separated by only one atomic row, i.e. so long as they do not coalesce they retain their individual magnetic properties.