Despite rapidly growing to immense sizes, virus populations suffer repeated severe bottlenecks, both within hosts and when transmitted from host to host. The potential effect of bottlenecks has been theoretically and experimentally documented, but formal estimations of their actual sizes in natural situations are scarce. Bottlenecks during colonization of organs and during transmission are influenced by those occurring at the cellular level. The study of the multiplicity of cellular infection (MOI) thus appears central, and this trait may be differentially regulated by different virus species. The values of MOI and their putative regulation deserve important future efforts, in order to disentangle the complex interactions between the control of gene copy numbers and the populations dynamics/genetics of viruses.