Craniofacial development comprises a complex process in humans in which failures or disturbances frequently lead to congenital anomalies. Cleft lip with/without palate (CL/P) is a common congenital anomaly that occurs due to variations in craniofacial development genes, and may occur as part of a syndrome, or more commonly in isolated forms (non-syndromic). The etiology of CL/P is multifactorial with genes, environmental factors, and their potential interactions contributing to the condition. Rehabilitation of CL/P patients requires a multidisciplinary team to perform the multiple surgical, dental, and psychological interventions required throughout the patient's life. Despite progress, lip/palatal reconstruction is still a major treatment challenge. Genetic mutations and polymorphisms in several genes, including extracellular matrix (ECM) genes, soluble factors, and enzymes responsible for ECM remodeling (e.g., metalloproteinases), have been suggested to play a role in the etiology of CL/P; hence, these may be considered likely targets for the development of new preventive and/or therapeutic strategies. In this context, investigations are being conducted on new therapeutic approaches based on tissue bioengineering, associating stem cells with biomaterials, signaling molecules, and innovative technologies. In this review, we discuss the role of genes involved in ECM composition and remodeling during secondary palate formation and pathogenesis and genetic etiology of CL/P. We also discuss potential therapeutic approaches using bioactive molecules and principles of tissue bioengineering for state-of-the-art CL/P repair and palatal reconstruction.