The evolution of complex organs is a source of controversy because they require the contributions of many adaptations to function properly. We argue that placentas are complex, that they have evolved multiple times in Poeciliopsis, and that there are closely related sister taxa that have either no placentas or intermediate stages in the evolution of a placenta. Furthermore, placentas can evolve in 750,000 years or less, on the same time scale as suggested by theoretical calculations for the evolution of complex eyes. Independent origins of such complexity, accompanied by sister taxa that either lack or have intermediate stages in the evolution of the trait, present an opportunity to study the evolution of novelty and complexity from a comparative, evolutionary perspective.