To accomplish regenerative medicine, several critical issues in stem cell biology have to be solved, including the identification of sources, the expanding population, building them into organs, and assimilating them to the host. Although many stem cells can now differentiate along certain lineages, knowledge on how to use them to build organs lags behind. Here we focus on topobiological events that bridge this gap, for example, the regulation of number, size, axes, shape, arrangement, and architecture during organogenesis. Rather than reviewing detail molecular pathways known to disrupt organogenesis when perturbed, we highlight conceptual questions at the topobiological level and ask how cellular and molecular mechanisms can work to explain these phenomena. The avian integument is used as the Rosetta stone because the molecular activities are linked to organ forms that are visually apparent and have functional consequences during evolution with fossil records and extant diversity. For example, we show that feather pattern formation is the equilibrium of stochastic interactions among multiple activators and inhibitors. Although morphogens and receptors are coded by the genome, the result is based on the summed physical-chemical properties on the whole cell's surface and is self-organizing. For another example, we show that developing chicken and duck beaks contain differently configured localized growth zones (LoGZs) and can modulate chicken beaks to phenocopy diverse avian beaks in nature by altering the position, number, size, and duration of LoGZs. Different organs have their unique topology and we also discuss shaping mechanisms of liver and different ways of branching morphogenesis. Multi-primordium organs (e.g., feathers, hairs, and teeth) have additional topographic specificities across the body surface, an appendage field, or within an appendage. Promises and problems in reconstitute feather/hair follicles and other organs are discussed. Finally, simple modification at the topobiological level may lead to novel morphology for natural selection at the evolution level.