The epitaxial growth and the structure of Cu on Si(111)7X7 was investigated by scanning tunneling microscopy (STM) and Auger electron spectroscopy. The so-called quasi-"5x5" incommensurate structure of Cu/Si(lll) was observed by STM with atomic resolution only probing the surface empty states with 2.5 V bias. STM analysis showed the "5 x 5" structure as made out of rounded shaped clusters with periodicity between 5.4a(Si) and 5.7a(Si) where a(Si) is the lattice parameter of the Si(lll)l X 1 surface. The quasi-"5 X 5" incommensurate structure was observed to grow layer by layer, and silicon atoms must be available for reacting with copper to form the two-dimensional (2D) incommensurate layer. The formation of the incommensurate quasi-"5 x 5" structure at room temperature was only observed on stepped crystals and is considered to be due to the consumption of silicon from the step edges. On 0 degrees miscut Si(lll) crystals, the quasi-"5 X 5" structure is formed upon thermal annealing, which is necessary to break the Si-Si bonds on the terrace. Films of about 2 ML of Cu/Si(lll) heated up to less than 800 K present a very interesting and uncommon arrangement. A first, a complete layer of the incommensurate structure is formed and over it a second layer of 2D crystals with irregular interfaces starts nucleating. Over these 2D crystals, more 2D crystals can grow. All the layers are composed of the same clusters and the periodicity of the arrangement can differ from layer to layer. The organized 2D crystals of the quasi-"5 x 5" layer grow upon annealing, and point defects and dislocations are formed to relieve stress coming from the incommensurability between the layer and the Si(lll) substrate. These defect lead to faults in the tiling of the clusters on the quasi-"5x5" layer. The formation of three-dimensional (3D) crystals made out of Cu3Si was also observed on 1-2 ML Cu/Si(lll) films annealed to temperatures above 950 K; their electronic structure is completely different from that of the incommensurate "5 X 5" structure.