The vertebrate brain and spinal cord arise from a common precursor, the neural tube, which forms very early during embryonic development. To shape the forming neural tube, changes in cellular architecture must be tightly co-ordinated in space and time. Live imaging of different animal models has provided valuable insights into the cellular dynamics driving neural tube formation. The most well-characterised morphogenetic processes underlying this transformation are convergent extension and apical constriction, which elongate and bend the neural plate. Recent work has focused on understanding how these two processes are spatiotemporally integrated from the tissue- to the subcellular scale. Various mechanisms of neural tube closure have also been visualised, yielding a growing understanding of how cellular movements, junctional remodelling and interactions with the extracellular matrix promote fusion and zippering of the neural tube. Additionally, live imaging has also now revealed a mechanical role for apoptosis in neural plate bending, and how cell intercalation forms the lumen of the secondary neural tube. Here, we highlight the latest research on the cellular dynamics underlying neural tube formation and provide some perspectives for the future.