The use of reduced models for investigating the self-assembly dynamics underlying protein shell formation in spherical viruses is described. The spontaneous self-assembly of these polyhedral, supramolecular structures, in which icosahedral symmetry is a conspicuous feature, is a phenomenon whose dynamics remain unexplored; studying the growth process by means of computer simulation provides access to the mechanisms underlying assembly. In order to capture the more universal aspects of self-assembly, namely the manner in which component shapes influence structure and assembly pathway, in this exploratory study low-resolution approximations are used to represent the basic protein building blocks. Alternative approaches involving both irreversible and reversible assembly are discussed, models based on both schemes are introduced, and examples of the resulting behavior described.