In this article, we review recent progress in the exploration of the complex magnetic phases of the fee Fe/Cu(111) system. In particular, we emphasize the magnetic properties realized by the synthesis of novel nanostructures of Fe on Cu(111). These include monolayer films, one-dimensional stripe arrays and nanodot arrays. The effects of spatial confinement, together with strong spin-lattice correlations, result in dramatically different magnetic behaviour for the various manifestations of the Fe/Cu(111) system. Multi-scale theoretical calculations have been used to provide an understanding of the magnetic behaviour in each case.