In the last few years, an understanding has emerged of the developmental mechanism for the consistent internal left-right structure, termed situs, that characterises vertebrate anatomy. This involves largely vertebrate-conserved (i.e. 'phylotypic') gene expression cascades that encode 'leftness' and 'rightness' in appropriate tissues either side of the embryo's midline soon after gastrulation. Recent evidence indicates that the initial, directional symmetry breaking that initiates these cascades utilises mechanisms that are conserved or at least closely related in different vertebrate types. I describe a scenario whereby the capacity for directional modification of an otherwise bilateral body plan can be viewed as an adaptive innovation rather closely connected with vertebrate origins, enabling optimal 'design' for very active lifestyles. But an alternative scenario, while retaining the view that situs and indeed other vertebrate functional lateralisations are deeply adaptive, proposes that they originated in the co-optation of left-right developmental information inherited from a very early stage in metazoan diversification. It is proposed that a remote chordate ancestor lost its original or 'ur-bilaterian' symmetry to pass through an altogether non-symmetrical stage, and that the vertebrate dorsoventral midline plane is not descended from that original one. I review the considerable evidence in favour of this scenario, and discuss its wider implications for directional asymmetries across the Metazoa.