The placenta is the only human organ that is discarded when it is no longer needed. It is also the only organ that is grown from scratch for each new pregnancy, since it derives from the embryo, and is thus not genetically part of the mother’s body. Its duty in providing nourishment for a growing fetus is highly specialized and short-lived. As an organ, the placenta is a key component of the interface between mother and fetus, regulating the transport of a range of atoms and molecules between two intrinsically distinct entities. Its primary role is to transport oxygen and nutrients from the mother’s blood to her growing fetus and to filter waste products from the fetus’s returning blood. While this intimacy enables fetal growth, it also means that undesirables in the maternal circulation may pass to the developing fetus, such as toxins or viruses. Because of its endocrine role in pregnancy, the placenta has an out-sized role in women’s health in addition to being absolutely critical to the health of a developing fetus in utero. However, the human placenta remains a “black box” that is difficult to study, since there are no adequate animal models that fully capture the human placenta’s structure and function and research involving pregnant women is limited. This gap in research methodologies requires the development of in vitro and in silico engineering approaches to model human placental function, utilizing engineering materials in both experimental and computational techniques. Here such biomaterials are considered in the context of organoids and tissue engineering, microphysiological systems, and for their role in computational modeling of placental function. This is a fast-growing and relatively recent field of research full of opportunities with potential to influence maternal and fetal outcomes.