Pulpal and periapical diseases account for a large proportion of dental visits, the current treatments for which are root canal therapy (RCT) and pulp revascularisation. Despite the clinical signs of full recovery and histological reconstruction, true regeneration of pulp tissues is still far from being achieved. The goal of regenerative endodontics is to promote normal pulp function recovery in inflamed or necrotic teeth that would result in true regeneration of the pulpodentinal complex. Recently, rapid progress has been made related to tissue engineering-mediated pulp regeneration, which combines stem cells, biomaterials, and growth factors. Since the successful isolation and characterisation of dental pulp stem cells (DPSCs) and other applicable dental mesenchymal stem cells, basic research and preclinical exploration of stem cell-mediated functional pulp regeneration via cell transplantation and cell homing have received considerably more attention. Some of this effort has translated into clinical therapeutic applications, bringing a ground-breaking revolution and a new perspective to the endodontic field. In this article, we retrospectively examined the current treatment status and clinical goals of pulpal and periapical diseases and scrutinized biological studies of functional pulp regeneration with a focus on DPSCs, biomaterials, and growth factors. Then, we reviewed preclinical experiments based on various animal models and research strategies. Finally, we summarised the current challenges encountered in preclinical or clinical regenerative applications and suggested promising solutions to address these challenges to guide tissue engineering-mediated clinical translation in the future.