Mesenchymal stem cells (MSCs) from bone marrow, adult organs and fetuses face the disadvantages of invasive isolation, limited cell numbers and ethical constraints while embryonic stem cells (ESCs) and induced pluripotent stem cells (iPSCs) face the clinical hurdles of potential immunorejection and tumorigenesis respectively. These challenges have prompted interest in the study and evaluation of stem cells from birth-associated tissues. The umbilical cord (UC) has been the most popular. Hematopoietic stem cells (HSCs) harvested from cord blood have been successfully used for the treatment of hematopoietic diseases. Stem cell populations have also been reported in other compartments of the UC viz., amnion, subamnion, perivascular region, Wharton's jelly, umbilical blood vessel adventia and endothelium. Differences in stemness characteristics between compartments have been reported and hence derivation protocols using whole UC pieces containing all compartments yield mixed stem cell populations with varied characteristics. Stem cells derived directly from the uncontaminated Wharton's jelly (hWJSCs) appear to offer the best clinical utility because of their unique beneficial properties. They are non-controversial, can be harvested painlessly in abundance, proliferative, possess stemness properties that last several passages in vitro, multipotent, hypoimmunogenic and do not induce tumorigenesis even though they have some ESC markers. hWJSCs and its extracts (conditioned medium and lysate) also possess anti-cancer properties and support HSC expansion ex vivo. They are thus attractive autologous or allogeneic agents for the treatment of malignant and non-malignant hematopoietic and non-hematopoietic diseases. This review critically evaluates their therapeutic value, the challenges and future directions for their clinical application.