Mesenchymal stem cells (MSCs) originating from the umbilical cord (UC) or Wharton's jelly (WJ) have attracted substantial interest due to their potential to augment therapeutic approaches for a wide range of disorders. These cells demonstrate a wide range of capabilities in the process of differentiating into a multitude of cell types. Additionally, they possess a significant capacity for proliferation and are conveniently accessible. Furthermore, they possess a status of being immune-privileged, exhibit minimal tumorigenic characteristics, and raise minimal ethical concerns. Consequently, they are well-suited candidates for tissue regeneration and the treatment of diseases. Additionally, UC-derived MSCs offer a substantial yield compared to other sources. The therapeutic effects of these MSCs are closely associated with the release of nanosized extracellular vesicles (EVs), including exosomes and microvesicles (MVs), containing lipids, microRNAs, and proteins that facilitate intercellular communication. Due to their reduced tumorigenic and immunogenic characteristics, in addition to their convenient manipulability, EVs have arisen as a viable alternative for the management of disorders. The favorable characteristics of UC-MSCs or WJ-MSCs and their EVs have generated significant attention in clinical investigations encompassing diverse pathologies. Therefore, we present a review encompassing current preclinical and clinical investigations, examining the implications of UC-MSCs in diverse diseases, including those affecting bone, cartilage, skin, liver, kidney, neural, lung, cardiovascular, muscle, and retinal tissues, as well as conditions like cancer, diabetes, sepsis, and others.