We study amphioxus (Cephalochordates), and developmental genes (Hox, ParaHox, BHLH, Neurotrophic factors and receptors among others) to investigate the fundamentals of genomic and morphological evolution at the invertebrate/vertebrate transition. If evolution is change in morphology, morphology depends on embryonic development, and embryonic development depends on developmental genes and gene networks, then studying the evolutionary changes in developmental genes and gene networks is the crux to understand evolution. As simple as it sounds, this is the challenge of the new discipline of Evolution and Development, or Evo-Devo: understanding the mechanisms unerlaying morphological evolution through changes in developmental programmes. We focus mainly (but not exclusively) in one of the major transitions of Metazoan Evolution, the origin of vertebrates. In such transition, several major events took place, as the origin of vertebrae, neural crests, paired appendages and sense organs, and the elaboration of complex brains. Amphioxus (Cephalochordates) are the closest extant relatives of vertebrates, with a simple, vertebrate-like body plan and a simple, pre-duplicative genome, devoid, unlike vertebrates, of genetic redundancy. We are studying genes and gene networks in amphioxus whose changes and co-options could have played a role in the advent of the former innovations. These include the Hox, ParaHox, Mox and other homeoboxes, plus genes involved in the complexity of the vertebrate nervous system., as Neurotrophic factors and receptors. Presently we are entering in the post-genomic era, with the amphioxus genome fully sequenced, and into the exciting and mysterious "experimental" "third wave" of Evo-Devo, that is the genetic modification of animals situated in key phylogenetic positions, to functionally test the genetic changes that comparative genetics points out to responsible for morphological innovations. We would like to test, among others, the origins of the neural crests, the origin of somites and skeleton, and the complexity of the nervous system. Unsure, risky, and (to us!) very exciting.