Textbook accounts of vertebrate embryonic development have been based largely upon experiments on amphibian embryos, which have shown that the tissues of the trunk and tail are organised from distinct precursors that existed during gastrulation. In the mouse and chick, however, retrospective clonal analyses and transplantation experiments have demonstrated that the amniote body instead arises progressively from a population of axial precursors that are common to both the neural and mesodermal tissues of the trunk and tail. For this reason, they are known as neuro-mesodermal progenitors (NMps). Detailed studies of NMps have been precluded by their lack of a unique gene expression profile and the technical difficulties associated with isolating them from the embryo. Mouse embryonic stem cells (ESCs) provide the possibility of instead deriving them in vitro. ESCs have been used to model developmental processes, partly through large cellular aggregates known as embryoid bodies. These structures do not, however, resemble the axial organisation of the embryo and they develop in a disordered manner. This thesis presents a novel culture system of small, three-dimensional aggregates of ESCs (gastruloids) that can recreate the events of early post-implantation development, including axial elongation. Gastruloids are the first ESC-based model for axial elongation morphogenesis; this body of work characterises their development and identifies a candidate population of NMps within their elongating tissues. Additionally, this work establishes a xenotransplantation assay for testing the functional properties of in vitro-derived NMp populations in the chicken embryo and applies it to NMps from gastruloid cultures. The results of this assay show that gastruloids are a credible source of NMps in vitro and therefore offer a new experimental means to interrogate their properties. The use of gastruloids to recreate embryonic development has implications for basic research as a synthetic system and for the therapeutic derivation of other embryonic progenitors through bioengineering.