The structures formed by growing a range of metals and semimetals on Cu{100} single crystal are investigated by quantitative low-energy electron-diffraction (LEED). Symmetrized Automated Tensor LEED (SATLEED) calculations are used to determine the structure of the surface alloys and overlayers formed. The Cu{100}/Pd system has been studied in the Pd coverage range 0.1-1.0 ML using SATLEED and Diffuse LEED (DLEED). Palladium atoms adsorb in the coverage range 0.1 < 0pd < 0.5 ML primarily by substitutional replacement of top layer copper atoms forming a two-dimensional CuxPd].x surface alloys leading to formation of an ordered Cu{100}-c(2x2)-Pd two-dimensional alloy at 0pa = 0.5 ML The kinetics and mechanism of an irreversible overlayer to underlayer transition in the Cu{100}-c(2x2)-Pd surface alloy (0pd = 0.5 ML) has been investigated. The activation energy for Pd site switching from the outermost layer to sub-surface (second layer) sites has been found to be 109±12 kJ mol'1 (1.13+0.12 eV). The structure of the underlayer alloy has been determined by SATLEED. Substitution of 0.5 ML of Pd into subsurface sites leads to significant expansion of the outermost two interlayer spacings Adzi2 = +3.3 ± 3.3 %, Adz23 = +6.6 ± 2.8 %. At monolayer coverage, Pd forms a double layer ordered c(2x2) CuPd alloy with p(2x2)-p2gg symmetry introduced into the outermost layer via clock rotation of the CuPd monolayer with the p(2x2) vertices centred over second layer Pd atoms. Lateral shifts of the top layer Cu and Pd atoms are determined to be 0.25+0.12A. The room temperature deposition of 0.5 ML Pt on Cu{100} followed by annealing to 525 K results an ordered c(2x2) Cu-Pt second layer capped with a pure Cu layer. The first and second interlayer spacings are found to be expanded by +5.1+1.7 % and +3.5+1.7%, respectively (relative to the bulk Cu interlayer spacing of 1.807 A) due to the insertion of the 8% larger Pt atoms into the second layer with Pt atoms rippled outwards towards the solid-vacuum interface by 0.08+0.06 A.