These rare facial diseases, which include hemifacial microsomia, Parry–Romberg syndrome, Moebius syndrome, Treacher Collins syndrome, Apert syndrome, and Crouzon syndrome, among others, pose considerable difficulties in diagnosis and treatment due to their clinical variability, rare occurrence, and complex genetic etiology. This review highlights the increasing potential of artificial intelligence (AI) and machine learning (ML) technologies in the better diagnosis, phenotyping, genotyping, and clinical management of these rare disorders. In this review, the applications of AI to facial phenotyping, three-dimensional (3D) imaging, radiomics, multimodal learning, and explainable AI have been highlighted. It also points out some latest developments in the field of bioinformatics, genome editing, RNA therapies, patient-derived models, and digital twin technology for precision medicine and translational research. Presently, there is sufficient evidence indicating the benefits of AI in increasing the accuracy in diagnosis, objective craniofacial evaluation, and customized treatment plans, whereas computational therapy is still experimental. However, various barriers such as data limitations, variability in phenotype, bias in the algorithms, external validation, ethical issues, and regulation prevent its widespread adoption in clinical practice. Future studies need to concentrate on multicenter data sharing, multimodal explainable AI, precision genomics, and translational framework to speed up the adoption of AI in rare craniofacial medicine.