The treatment/regeneration of bone and cartilage diseases or defects, whether induced by rheumatism, joint dysplasia, trauma, or surgery presents great challenges that have not been fully solved by the current therapies. In the last few years, tissue engineering and regenerative medicine have been proposing advanced tools and technologies for bone and cartilage tissue regeneration, and some of which have successfully reached the market. Beyond the source of cells, the creation of superior structures for replacing defective bone and cartilage requires strong research in biomechanical signaling and synthesis of advanced biomaterials to mimic human tissues at the most varied levels. Natural and synthetic polymers, bioresorbable inorganic materials, and composites have been investigated for its potential as scaffolding materials with enhanced mechanical and biological properties. Porous scaffolds, hydrogels, and fibers are the most commonly biomimetic structures used for bone and cartilage tissue engineering. Herein, the concepts and current treatment strategies for bone and cartilage repair, as well as biomimetic strategies for bone and cartilage tissue engineering are overviewed. A global review of the ongoing clinical trials and of the scaffolds commercially available for the repair of osteochondral tissue is also presented.