How organs originate and evolve is a question fundamental to understanding the evolution of complex multicellular life forms. Vertebrates have a relatively standard body plan with more or less the same conserved set of organs. The placenta is a comparatively more recently evolved organ, derived in many lineages independently. Using placentas as a model, we discuss the genetic basis for organ origins. We show that the evolution of placentas occurs by acquiring new functional attributes to existing tissues, changes in the patterning and development of tissues, and the evolution of novel cell types. We argue that a diversity of genomic changes facilitated these physiological transformations and that these changes are likely to have occurred during the evolution of organs more broadly. Finally, we argue that a key aspect to understanding the evolutionary origin of organs is that they are likely to result from novel interactions between distinct cell populations.