Genetic conditions, traumatic injuries, carious lesions and periodontal diseases are all responsible for dental pathologies. The current clinical approaches are based on the substitution of damaged dental tissues with inert materials, which, however, do not ensure full physiological recovery of the teeth. Different populations of dental mesenchymal stem cells have been isolated from dental tissues and several attempts have already been made at using these stem cells for the regeneration of human dental tissues. Despite encouraging progresses, dental regenerative therapies are very far from any clinical applications. This is tightly connected with the absence of proper platforms that would model and faithfully mimic human dental tissues in their complexity. Therefore, in the last decades, many efforts have been dedicated for the development of innovative systems capable of emulating human tooth physiology in vitro. This review focuses on the use of in vitro culture systems, such as bioreactors and “organ-on-a-chip” microfluidic devices, for the modelling of human dental tissues and their potential use for dental regeneration and drug testing.