During organogenesis, various molecular and physical signals are orchestrated in space and time to sculpt multiple cell types into functional tissues and organs. The complex and dynamic nature of the process has hindered studies aimed at delineating morphogenetic mechanisms in vivo, particularly in mammals. Recent demonstrations of stem cell-driven tissue assembly in culture offer a powerful new tool for modeling and dissecting organogenesis. However, despite the highly organotypic nature of stem cell-derived tissues, substantial differences set them apart from their in vivo counterparts, probably owing to the altered microenvironment in which they reside and the lack of mesenchymal influences. Advances in the biomaterials and microtechnology fields have, for example, afforded a high degree of spatiotemporal control over the cellular microenvironment, making it possible to interrogate the effects of individual microenvironmental components in a modular fashion and rapidly identify organ-specific synthetic culture models. Hence, bioengineering approaches promise to bridge the gap between stem cell-driven tissue formation in culture and morphogenesis in vivo, offering mechanistic insight into organogenesis and unveiling powerful new models for drug discovery, as well as strategies for tissue regeneration in the clinic. We draw on several examples of stem cell-derived organoids to illustrate how bioengineering can contribute to tissue formation ex vivo. We also discuss the challenges that lie ahead and potential ways to overcome them.