Here we reconstruct phylogenies describing the evolution of proteomes and protein domain structures of cellular organisms and double-stranded DNA viruses with medium-to-very-large proteomes (giant viruses). Trees of proteomes define viruses as a 'fourth supergroup' along with superkingdoms Archaea, Bacteria, and Eukarya. Trees of domains indicate they have evolved via massive and primordial reductive evolutionary processes. The distribution of domain structures suggests giant viruses harbor a significant number of protein domains including those with no cellular representation. The genomic and structural diversity embedded in the viral proteomes is comparable to the cellular proteomes of organisms with parasitic lifestyles. Since viral domains are widespread among cellular species, we propose that viruses mediate gene transfer between cells and crucially enhance biodiversity.