We study, by computational chemistry, atomic clusters that range in size from 3 atoms to thousands of atoms. The geometric structure and properties of small clusters are very different from those of the corresponding bulk materials. For example, silver clusters are not fragments of the fcc crystal, and clusters of rhodium are magnetic. We calculate, by a combination a density functional theory (DFT) and global optimization techniques, likely equilibrium structures of small clusters. Our theoretical predictions of vibrational spectra and electron detachment energies are compared to experiment for structure elucidation. We try to understand the factors controlling stability, so that we might predict cluster sizes and compositions that are particularly stable. We model surfaces and noncrystalline materials with clusters having a hundred or more atoms. We use more approximate theoretical models for these larger clusters, such as empirical potentials and model hamiltonians. We are interested in new computational techniques for electronic structure, global optimization, and simulation of systems with large numbers of atoms.