The capsids of most spherical viruses are icosahedral, an arrangement of multiples of 60 subunits. Though it is a salient point in the life cycle of any virus, the physical chemistry of virus capsid assembly is poorly understood. We have developed general models of capsid assembly that describe the process in terms of a cascade of low order association reactions. The models predict sigmoidal assembly kinetics, where intermediates approach a low steady state concentration for the greater part of the reaction. Features of the overall reaction can be identified on the basis of the concentration dependence of assembly. In simulations, and on the basis of our understanding of the models, we find that nucleus size and the order of subsequent "elongation" reactions are reflected in the concentration dependence of the extent of the reaction and the rate of the fast phase, respectively. The reaction kinetics deduced for our models of virus assembly can be related to the assembly of any "spherical" polymer. Using light scattering and size exclusion chromatography, we observed polymerization of assembly domain dimers of hepatitis B virus (HBV) capsid protein. Empty capsids assemble at a rate that is a function of protein concentration and ionic strength. The kinetics of capsid formation were sigmoidal, where the rate of the fast phase had second-power concentration dependence. The extent of assembly had third-power concentration dependence. Simulations based on the models recapitulated the concentration dependences observed for HBV capsid assembly. These results strongly suggest that in vitro HBV assembly is nucleated by a trimer of dimers and proceeds by the addition of individual dimeric subunits. On the basis of this mechanism, we suggest that HBV capsid assembly could be an important target for antiviral therapeutics.