Mesenchymal stem or stromal cells (MSC) have proven to offer great promise for cell-based therapies and tissue engineering applications, as these cells are capable of extensive self-renewal and display a multilineage differentiation potential. Furthermore, MSC were shown to exhibit immunomodulatory properties and display supportive functions through parakrine effects. Besides bone marrow (BM), still today the most common source of MSC, these cells were found to be present in a variety of postnatal and extraembryonic tissues and organs as well as in a large variety of fetal tissues. Over the last decade, the human umbilical cord and human amnion have been found to be a rich and valuable source of MSC that is bio-equivalent to BM-MSC. Since these tissues are discarded after birth, the cells are easily accessible without ethical concerns.