One of the most remarkable processes in biology is how animals develop from a single fertilized egg within a short time of rapid growth and an explosion in spatial and cellular diversity. Embryonic development is highly deterministic and consistent among different embryos and conserved across species. Astonishingly, embryos reuse the same signaling pathways in diverse developmental contexts to robustly pattern tissues. The advent of single-cell genomics in the last decade has allowed to chart the phenomenology of cellular differentiation at unprecedented resolution and scale. Yet, moving from such single-cell descriptions to models of how embryonic tissues achieve robustness and precision in their differentiation remains exceedingly difficult. To this end, we will develop new algorithms that will infer the spatiotemporal dynamics of differentiating tissues from space-, time- and lineage-resolved data. Tissues will be modelled as groups of proliferating and interacting cells distributed in space and moving along transcriptional, epigenetic and signaling manifolds. Focusing on the developmental stages of gastrulation and early organogenesis, we will reconstruct the spatiotemporal trajectories of cells together with the dynamics of their local niches. These trajectories will serve as the input to mathematical models that will predict local changes in a cell’s state from its signalome, epigenome and transcription factor repertoire. Using zebrafish embryos as a high-throughput system of vertebrate development, we will systematically test these models through time-dependent, combinatorial perturbations with a multiomic read-out. My overall goal is to develop quantitative, data-based models of how transcriptional, epigenetic and intercellular changes at the cellular level translate into robust and deterministic dynamics at the tissue level and to apply these methods to dissect how positional information and cell fate commitment emerges in the vertebrate embryo.