Mesenchymal stem/stromal cells (MSC) are promising candidates for use in cell-based therapies. In most cases, therapeutic response appears to be cell-dose dependent. Human term placenta is rich in MSC and is a physically large tissue that is generally discarded following birth. Placenta is an ideal starting material for the large-scale manufacture of multiple cell doses of allogeneic MSC. The placenta is a fetomaternal organ from which either fetal or maternal tissue can be isolated. This article describes the placental anatomy and procedure to dissect apart the decidua (maternal), chorionic villi (fetal), and chorionic plate (fetal) tissue. The protocol then outlines how to isolate MSC from each dissected tissue region, and provides representative analysis of expanded MSC derived from the respective tissue types. These methods are intended for pre-clinical MSC isolation, but have also been adapted for clinical manufacture of placental MSC for human therapeutic use.