Recent examples have highlighted how stem cells have the capability to initiate morphogenesis in vitro; that is, to generate complex structures in culture that closely parallel their in vivo counterparts. Lgr5, the receptor for the Wnt-agonistic R-spondins, marks stem cells in multiple adult organs of mice and humans. In R-spondin-based three-dimensional cultures, these Lgr5 stem cells can grow into ever-expanding epithelial organoids that retain their original organ identity. Single Lgr5 stem cells derived from the intestine can be cultured to build epithelial structures that retain hallmarks of the in vivo epithelium. Here, we review the mechanisms that support this notable example of self-organization and discuss applications of this technology for stem cell research, disease modeling (e.g., for colorectal cancer and cystic fibrosis), and regenerative medicine.