The structures of pure gold and silver clusters (Au-k, Ag-k, k = 1-13) and neutral and anionic gold-silver binary clusters (AumAgn, 2 less than or equal to k = m + n less than or equal to 7) have been investigated by using density functional theory (DFT) with generalized gradient approximation (GGA) and high level ab initio calculations including coupled cluster theory with relativistic ab initio pseudopotentials. Pure Auk clusters favor 2-D planar configurations, while pure Ag-k clusters favor 3-D structures. In the case of Au, the valence orbital energies of 5d are close to that of 6s. This allows the hybridization of 6s and 5d orbitals in favor of planar structures of Au-k clusters. Even 1-D linear structures show reasonable stability as local minima (or as global minima in a few small anionic clusters). This explains the ductility of gold. On the other hand, the Ag-4d orbital has a much lower energy than the 5s. This prevents hybridization, and so the coordination number (Nc) of Ag in Ag-k tends to be large in s-like spherical 3-D coordination in contrast to that of An in Auk which tends to be small in 1-D or 2-D coordination. This trend is critical in determining the cluster structures. The calculated electronic properties and dissociation energy of both pure and binary clusters are in good agreement with the available experimental data. Since the Ag-5s orbital is much higher in energy than the Au-6s orbital energy, the partial charge transfer from Au to Ag takes place in- gold-silver binary clusters. Au atoms tend to be negatively charged, while Ag atoms tend to be positively charged. Combined with the trend that An atoms favor the surface, edges, or vertices with smaller Nc, the outer part of the cluster tends to be negatively charged, while Ag atoms favor the inside with larger Nc, and so the inner part tends to be positively charged. The partial charge transfer in the binary system results in electrostatic energy gain for the binary AumAgn cluster over pure Auk and Ag-k clusters, which is responsible for the formation of alloys. In a neutral alloy, the equivalent mixing is favored, and the even numbered k tends to be more stable due to the electron spin pairing, whereas in an anionic alloy the odd numbered k tends to be more stable.