Craniofacial bone defect anomalies affect both soft and hard tissues and can be caused by trauma, bone recessions from tumors and cysts, or even from congenital disorders. On this note, cleft/lip palate is the most prevalent congenital craniofacial defect caused by disturbed embryonic development of soft and hard tissues around the oral cavity and face area, resulting in most cases, of severe limitations with chewing, swallowing, and talking as well as problems of insufficient space for teeth, proper breathing, and self-esteem problems as a consequence of facial appearance. Spectacular advances in regenerative medicine have arrived, giving new hope to patients that can benefit from new tissue engineering therapies based on the supportive action of 3D biomaterials together with the synergic action of osteo-inductive molecules and recruited stem cells that can be driven to the process of bone regeneration. However, few studies have focused on the application of tissue engineering to the regeneration of the cleft/lip and only a few have reported significant advances to offer real clinical solutions. This review provides an updated and deep analysis of the studies that have reported on the use of advanced biomaterials and cell therapies for the regeneration of cleft lip and palate regeneration.