A clonally diverse anticipatory repertoire in which each lymphocyte bears a unique antigen receptor is the central feature of the adaptive immune system that evolved in our vertebrate ancestors. The survival advantage gained through adding this type of adaptive immune system to a pre-existing innate immune system led to the evolution of alternative ways for lymphocytes to generate diverse antigen receptors for use in recognizing and repelling pathogen invaders. All jawed vertebrates assemble their antigen-receptor genes through recombinatorial rearrangement of different immunoglobulin or T cell receptor gene segments. The surviving jawless vertebrates, lampreys and hagfish, instead solved the receptor diversification problem by the recombinatorial assembly of leucine-rich-repeat genetic modules to encode variable lymphocyte receptors. The convergent evolution of these remarkably different adaptive immune systems involved innovative genetic modification of innate-immune-system components.