The behavior of stem cells, when they work collectively, can be much more sophisticated than one might expect from their individual programming. This Perspective covers recent discoveries about the dynamic patterning and structural self-formation of complex organ buds in 3D stem cell culture, including the generation of various neuroectodermal and endodermal tissues. For some tissues, epithelial-mesenchymal interactions can also be manipulated in coculture to guide organogenesis. This new area of stem cell research—the spatiotemporal control of dynamic cellular interactions—will open a new avenue for next-generation regenerative medicine.