The life quality of patients with craniofacial malformations is severely affected by the physical disabilities caused by the malformation itself, but also by being subjected to bullying, which leads to a series of relevant psychological and societal effects that have an economic impact on the health sector. Orofacial clefts, notably cleft lip (CL), cleft palate, and microtia, are the most common craniofacial birth defects in humans and represent a substantial burden, both personal and societal. On the other hand, osteoarthritis is a widespread degenerative disease that is becoming more common due to the extension of the human lifespan and to an increase in injuries in young people as a result of their lifestyle. Advances in tissue engineering as a part of regenerative medicine offer new hope to patients that can benefit from new tissue engineering therapies based on the supportive action of tailored 3D biomaterials and the synergic action of stem cells that can be driven to the process of bone and cartilage regeneration. This review provides an update on recent considerations for stem cells and studies on the use of advanced biomaterials and cell therapies for the regeneration of craniofacial congenital malformations and articular degenerative diseases.