Human beings have a natural interest in their origins. We are vertebrates, within the craniates, within the chordates. Fossils indicate how the chordates separated, in early Palaeozoic times or before, from their latest common ancestor with the echinoderms. The most primitive known fossil chordates retained a calcitic skeleton of echinoderm type (calcichordates) and some of these, the mitrates, were like giant calcite-plated tunicate tadpoles, consisting of a head and a tail with no trunk region. Some mitrates are themselves craniates in the broad sense and represent the ancestral group (stem group) from which extant craniates descended. In this paper, we describe such a stem-craniate mitrate, and reconstruct, from the shared characteristics of the extant craniates supplemented by evidence from fossils, the latest common ancestor of extant craniates which we call "animal x" . (In most respects animal x would resemble a hagfish, but its larva would filter-feed like a lamprey larva.) We then list the changes involved in transforming a mitrate into animal x and describe the probable changes in development in early embryos that converted a mitrate into animal x. During this transition, our ancestors took to swimming forwards rather than crawling rearwards, lost the calcitic skeleton, and acquired the trunk region, the notochordal region to the head, kidneys, and neural-crest cartilage. An important developmental mechanism involved was forward extension of the notochord, caused by anteriorly directed convergent extension movements.