Cartilage diseases and injuries are considered difficult to treat owing to the low regenerative capacity of this tissue. Using stem cells (SCs) is one of the potential methods of treating cartilage defects and creating functional cartilage models for transplants. Their ability to proliferate and to generate functional chondrocytes, a natural tissue environment, and extracellular cartilage matrix, makes SCs a new opportunity for patients with articular injuries or incurable diseases, such as osteoarthritis (OA). The review summarizes the most important scientific reports on biology and mechanisms of SC-derived chondrogenesis and sources of SCs for chondrogenic purposes. Additionally, it focuses on the genetic mechanisms, microRNA (miRNA) regulation, and epigenetic processes steering the chondrogenic differentiation of SCs. It also describes the attempts to create functional cartilage with tissue engineering using growth factors and scaffolds. Finally, it presents the challenges that researchers will have to face in the future to effectuate SC differentiation methods into clinical practice for treating cartilage diseases.