The purpose of this article is twofold: to define briefly the state of the art of theoretical approaches to electronic, structural and thermal properties of small aggregates of metals and semiconductor elements, and to present new (sometimes preliminary) results of computer simulations on silicon, sodium and gold clusters. In particular, these calculations use the unified-molecular-dynamics-density-functional (Car-Parrinello) method for clusters of very small size (Si_N and Na_N with N up to 10), and effective many-body potentials for the gold clusters of larger size (N up to 1000). The connection between experiments and theory is discussed critically.