In this paper, we shall examine the evolution of domain architectures across 62 genomes of known phylogeny including all kingdoms of life. We look in particular at the possibility of convergent evolution, with a view to determining the extent to which the architectures observed in the genomes are due to functional necessity or evolutionary descent. We used domains of known structure, because from this and other information we know their evolutionary relationships. We use a range of methods including phylogenetic grouping, sequence similarity/alignment, mutation rates and comparative genomics to approach this difficult problem from several angles.