Dental, oral, and craniofacial (DOC) regenerative medicine aims to repair or regenerate DOC tissues including teeth, dental pulp, periodontal tissues, salivary gland, temporomandibular joint (TMJ), hard (bone, cartilage), and soft (muscle, nerve, skin) tissues of the craniofacial complex. Polymeric materials have a broad range of applications in biomedical engineering and regenerative medicine functioning as tissue engineering scaffolds, carriers for cell-based therapies, and biomedical devices for delivery of drugs and biologics. The focus of this review is to discuss the properties and clinical indications of polymeric scaffold materials and extracellular matrix technologies for DOC regenerative medicine. More specifically, this review outlines the key properties, advantages and drawbacks of natural polymers including alginate, cellulose, chitosan, silk, collagen, gelatin, fibrin, laminin, decellularized extracellular matrix, and hyaluronic acid, as well as synthetic polymers including polylactic acid (PLA), polyglycolic acid (PGA), polycaprolactone (PCL), poly (ethylene glycol) (PEG), and Zwitterionic polymers. This review highlights key clinical applications of polymeric scaffolding materials to repair and/or regenerate various DOC tissues. Particularly, polymeric materials used in clinical procedures are discussed including alveolar ridge preservation, vertical and horizontal ridge augmentation, maxillary sinus augmentation, TMJ reconstruction, periodontal regeneration, periodontal/peri-implant plastic surgery, regenerative endodontics. In addition, polymeric scaffolds application in whole tooth and salivary gland regeneration are discussed.