This review encompasses different pre-clinical bioengineering approaches for periodontal tissues, maxillary jaw bone, and the entire tooth. Moreover, it sheds light on their potential clinical therapeutic applications in the field of regenerative medicine. Herein, the electrospinning method for the synthesis of polycaprolactone (PCL) membranes, that are capable of mimicking the extracellular matrix (ECM), has been described. Furthermore, their functionalization with cyclosporine A (CsA), bone morphogenetic protein-2 (BMP-2), or anti-inflammatory drugs’ nanoreservoirs has been demonstrated to induce a localized and targeted action of these molecules after implantation in the maxillary jaw bone. Firstly, periodontal wound healing has been studied in an induced periodontal lesion in mice using an ibuprofen-functionalized PCL membrane. Thereafter, the kinetics of maxillary bone regeneration in a pre-clinical mouse model of surgical bone lesion treated with BMP-2 or BMP-2/Ibuprofen functionalized PCL membranes have been analyzed by histology, immunology, and micro-computed tomography (micro-CT). Furthermore, the achievement of innervation in bioengineered teeth has also been demonstrated after the co-implantation of cultured dental cell reassociations with a trigeminal ganglia (TG) and the cyclosporine A (CsA)-loaded poly(lactic-co-glycolic acid) (PLGA) scaffold in the jaw bone. The prospective clinical applications of these different tissue engineering approaches could be instrumental in the treatment of various periodontal diseases, congenital dental or cranio-facial bone anomalies, and post-surgical complications.