Density functional theory (DFT) calculations were carried out to explore the geometric, spectroscopic, and electronic properties of three magic silver clusters Agn (n = 8, 18, and 20) in detail. The computed results show that the global minima of these clusters are compact, near-spherical structures, while other low-lying isomers exhibit oblate or prolate shapes. Vertical ionization energies for the low-lying isomers were also computed and assigned with respect to available experimental values. Although several isomers were predicted to have similar energies, their electronic and vibrational signatures were quite distinctive, meaning that they could be used as fingerprint signals to distinguish between isomers. In addition, the electronic structures of these systems were explored using the phenomenological shell model. Calculations for the coinage metal clusters M20 (M = Cu, Ag, Au) indicated that the structures and properties of the Ag cluster are similar to those of the Cu cluster in that both Cu20 and Ag20 prefer a compact structure whereas Au20 prefers to adopt a tetrahedral form.