First principles calculations and simulations based on interatomic potentials together with experimental studies of abundance spectrum suggest icosahedral structures to be common for some magic clusters of diverse systems such as rare gases, metals, covalently bonded systems and water. Close packing models obtained from pair potentials are shown to be good representations of the structure of rare gas clusters. However, the electronic structure is found to play the important role in the atomic structure and related properties of other clusters. Results of recent studies of fullerenes, their derivatives as well as some large icosahedral metal clusters containing several thousand atoms are also presented. Further results on doped icosahedral clusters are discussed which hold promise for the development of new materials and for understanding the occurrence of icosahedral order in several aluminum alloys.