In recent years, stem cell-based models that reconstruct mouse and human embryogenesis have gained significant traction due to their near-physiological similarity to natural embryos. Embryo models can be generated in large numbers, provide accessibility to a variety of experimental tools such as genetic and chemical manipulation, and confer compatibility with automated readouts, which permits exciting experimental avenues for exploring the genetic and molecular principles of self-organization, development, and disease. However, the current embryo models recapitulate only snapshots within the continuum of embryonic development, allowing the progression of the embryonic tissues along a specific direction. Hence, to fully exploit the potential of stem cell-based embryo models, multiple important gaps in the developmental landscape need to be covered. These include recapitulating the lesser-explored interactions between embryonic and extraembryonic tissues such as the yolk sac, placenta, and the umbilical cord; spatial and temporal organization of tissues; and the anterior patterning of embryonic development. Here, it is detailed how combinations of stem cells and versatile bioengineering technologies can help in addressing these gaps and thereby extend the implications of embryo models in the fields of cell biology, development, and regenerative medicine.