Cell fate specification and chromatin regulation are central to developmental and stem cell biology. These processes have been mainly studied in animal models where mouse pluripotent stem cells have been key to characterise the molecular regulators of cell identity, chromatin states and gene expression during development and reprogramming. We are using human naive pluripotent stem cells as a model system for early human development, to characterise primate-specific cell fate specification events, gene regulatory programs and the genetic and epigenetic regulators underlying early human embryogenesis. We are particularly interested in developing and using novel stem-cell embryo models and single-cell technologies to reveal the gene regulatory logic underlying cell fate specification and gene regulation in early human embryogenesis. In this talk, I will present evidence that chromatin mechanisms oppose the induction of alternative cell fates in human naive pluripotent stem cells and in human blastoids. I will discuss experiments in human embryos that attempt to establish the predictability of human stem-cell embryo models to understand human development. Excitingly, I will also show that human naive pluripotent stem cells model the primate-specific development of the extraembryonic mesoderm, a key but little understood lineage of the early postimplantation primate embryo. Together, our work establishes that chromatin mechanisms oppose the induction of alternative cell fates in human naive pluripotent stem cells and provide a starting point to further model early human embryogenesis.