The capsids of spherical (icosahedral) viruses are constructed of multiples of 60 subunits. The question of how these polymers assemble is basic to understanding the viral life cycle. A formalism describing virus assembly as an equilibrium between coat protein subunits, assembly intermediates and intact virus is presented. This equilibrium model of virus assembly is consistent with experimental observations of virus assembly. At equilibrium, either intact virus or free subunits are dominant species, assembly intermediates are predicted to be found only in trace concentrations. The concentration of assembled virus at equilibrium is expected to be extremely concentration-dependent and resemble a highly cooperative reaction although the model does not explicitly include cooperativity. For statistical assembly of a polyhedron, a nucleus is not necessarily required and polymerization can proceed through a cascade of bimolecular reactions rather than a single higher order reaction. Thus, kinetics of assembly do not necessarily show the extreme concentration dependence typical of nucleated protein polymerization. Modest intersubunit interaction energies result in a very stable capsid; consequently, a small change in this interaction energy can result in a considerable change in the capsid-subunit equilibrium. Some possible effects of nucleation and protein-nucleic acid interactions on virus assembly and capsid morphology are considered.