Pluripotent stem cells are increasingly used to model different aspects of embryogenesis and organ formation1. Despite recent advances in in vitro induction of major mesodermal lineages and cell types2,3, experimental model systems that can recapitulate more complex features of human mesoderm development and patterning are largely missing. Here we used induced pluripotent stem cells for the stepwise in vitro induction of presomitic mesoderm and its derivatives to model distinct aspects of human somitogenesis. We focused initially on modelling the human segmentation clock, a major biological concept believed to underlie the rhythmic and controlled emergence of somites, which give rise to the segmental pattern of the vertebrate axial skeleton. We observed oscillatory expression of core segmentation clock genes, including HES7 and DKK1, determined the period of the human segmentation clock to be around five hours, and demonstrated the presence of dynamic travelling-wave-like gene expression in in vitro-induced human presomitic mesoderm. Furthermore, we identified and compared oscillatory genes in human and mouse presomitic mesoderm derived from pluripotent stem cells, which revealed species-specific and shared molecular components and pathways associated with the putative mouse and human segmentation clocks. Using CRISPR-Cas9-based genome editing technology, we then targeted genes for which mutations in patients with segmentation defects of the vertebrae, such as spondylocostal dysostosis, have been reported (HES7, LFNG, DLL3 and MESP2). Subsequent analysis of patient-like and patient-derived induced pluripotent stem cells revealed gene-specific alterations in oscillation, synchronization or differentiation properties. Our findings provide insights into the human segmentation clock as well as diseases associated with human axial skeletogenesis.