Icosahedral geometry plays an important role in the structure and bonding, as well as the nucleation and growth, of many cluster systems. In particular, metal clusters containing Groups 10 and 11 metals tend to form partial or complete icosahedral structures. The tendency of clusters to adopt icosahedral or icosahedron-based structures may be termed ‘icosahedricity’. The formation of the closed-shell (13-atom) centered icosahedral structure marks the end of the nucleation process and the beginning of growth processes. One particular pathway is the ‘cluster of clusters’ growth whereby multiple icosahedral units are fused together via sharing of vertex atoms, giving rise to the polyicosahedral cluster series. This tendency to form polyicosahedral clusters has been coined ‘polyicosahedricity’. In this paper, attempts will be made to understand the role(s) that stereochemical and electronic effects play in the nucleation and growth of these icosahedral or icosahedron-based clusters, as well as the interrelationships between electron counts and cluster topologies. Other cluster growth pathways and their electronic requirements will also be discussed. We believe that icosahedricity and polyicosahedricity are important in the nucleation and growth, respectively, of many metal cluster systems where metal-metal bonding plays an important role in the cluster formation.