Bone marrow-derived mesenchymal stem cells (BM-MSCs) have been used for allogeneic application in tissue engineering but have certain drawbacks. Therefore, mesenchymal stem cells (MSCs) derived from other adult tissue sources have been considered as an alternative. The human umbilical cord and placenta are easily available noncontroversial sources of human tissue, which are often discarded as biological waste, and their collection is noninvasive. These sources of MSCs are not subjected to ethical constraints, as in the case of embryonic stem cells. MSCs derived from umbilical cord and placenta are multipotent and have the ability to differentiate into various cell types crossing the lineage boundary towards endodermal lineage. The aim of this chapter is to provide a detailed reproducible cookbook protocol for the isolation, propagation, characterization, and differentiation of MSCs derived from human umbilical cord and placenta with special reference to harnessing their potential towards pancreatic/islet lineage for utilization as a cell therapy product. We show here that mesenchymal stromal cells can be extensively expanded from umbilical cord and placenta of human origin retaining their multilineage differentiation potential in vitro. Our report indicates that postnatal tissues obtained as delivery waste represent a rich source of mesenchymal stromal cells, which can be differentiated into functional islets employing three-stage protocol developed by our group. These islets could be used as novel in vitro model for screening hypoglycemics/insulin secretagogues, thus reducing animal experimentation for this purpose and for the future human islet transplantation programs to treat diabetes.