Musculoskeletal disorders represent a major cause of disability and morbidity globally and result in enormous costs for health and social care systems. Development of cell-based therapies is rapidly proliferating in a number of disease areas, including musculoskeletal disorders. Novel biological therapies that can effectively treat joint and spine degeneration are high priorities in regenerative medicine. Mesenchymal stem cells (MSCs) isolated from bone marrow (BM-MSCs), adipose tissue (AD-MSCs) and umbilical cord (UC-MSCs) show considerable promise for use in cartilage and intervertebral disc (IVD) repair. This review article focuses on stem cell-based therapeutics for cartilage and IVD repair in the context of the rising global burden of musculoskeletal disorders. We discuss the biology MSCs and chondroprogenitor cells and specifically focus on umbilical cord/Wharton's jelly derived MSCs and examine their potential for regenerative applications. We also summarize key components of the molecular machinery and signaling pathways responsible for the control of chondrogenesis and explore biomimetic scaffolds and biomaterials for articular cartilage and IVD regeneration. This review explores the exciting opportunities afforded by MSCs and discusses the challenges associated with cartilage and IVD repair and regeneration. There are still many technical challenges associated with isolating, expanding, differentiating, and pre-conditioning MSCs for subsequent implantation into degenerate joints and the spine. However, the prospect of combining biomaterials and cell-based therapies that incorporate chondrocytes, chondroprogenitors and MSCs leads to the optimistic view that interdisciplinary approaches will lead to significant breakthroughs in regenerating musculoskeletal tissues, such as the joint and the spine in the near future.