Computer simulations have been playing an important role in understanding the evolution of structure, thermodynamic behaviour and other physicochemical properties of clusters. These studies have complemented experimental results and helped to develop basic concepts. In addition, it has become possible to do computer experiments to design new stable clusters with certain desired properties. Possibilities are being explored to ascertain whether certain magic clusters might be assembled to form solids. This could lead to the development of novel cluster-based materials. Here we review the progress in our understanding of the structural, electronic, magnetic and thermodynamic properties of clusters of metals and semiconductors, as well as mixed clusters. First principles approaches based on density functional theory have become central to such studies and a brief overview is given of widely used methods, such as those based upon a localized basis or a plane wave approach. Recent progress in transferable tight-binding parameter schemes is also discussed. Large metal clusters having up to several thousand atoms have been studied using simpler methods, such as the embedded-atom or the effective medium theory and results of some such studies are included.