Urochordates (ascidians) have recently supplanted cephalochordates (amphioxus) as the extant sister taxon of vertebrates. Given that urochordates possess migratory cells that have been classified as 'neural crest-like'- and that cephalochordates lack such cells--this phylogenetic hypothesis may have significant implications with respect to the origin of the neural crest and neural crest-derived skeletal tissues in vertebrates. We present an overview of the genes and gene regulatory network associated with specification of the neural crest in vertebrates. We then use these molecular data--alongside cell behaviour, cell fate and embryonic context--to assess putative antecedents (latent homologues) of the neural crest or neural crest cells in ascidians and cephalochordates. Ascidian migratory mesenchymal cells--non-pigment-forming trunk lateral line cells and pigment-forming 'neural crest-like cells' (NCLC)--are unlikely latent neural crest cell homologues. Rather, Snail-expressing cells at the neural plate of border of urochordates and cephalochordates likely represent the extent of neural crest elaboration in non-vertebrate chordates. We also review evidence for the evolutionary origin of two neural crest-derived skeletal tissues--cartilage and dentine. Dentine is a bona fide vertebrate novelty, and dentine-secreting odontoblasts represent a cell type that is exclusively derived from the neural crest. Cartilage, on the other hand, likely has a much deeper origin within the Metazoa. The mesodermally derived cellular cartilages of some protostome invertebrates are much more similar to vertebrate cartilage than is the acellular 'cartilage-like' tissue in cephalochordate pharyngeal arches. Cartilage, therefore, is not a vertebrate novelty, and a well-developed chondrogenic program was most likely co-opted from mesoderm to the neural crest along the vertebrate stem. We conclude that the neural crest is a vertebrate novelty, but that neural crest cells and their derivatives evolved and diversified in a step-wise fashion--first by elaboration of neural plate border cells, then by the innovation or co-option of new or ancient metazoan cell fates.