Introduction: Regenerative medicine offers innovative approaches to restore damaged tissues on the basis of tissue engineering (TE). Although research on advanced therapy medicinal products (ATMPs) has been very active in recent years, the number of licensed products remains surprisingly low and restricted to the treatment of severe, incurable diseases. Methods: This paper provides a critical review of current literature on the regulatory, clinical, and commercial status of ATMP-based therapies in the EU and worldwide and the hurdles to overcome for their broader application in Regenerative Dentistry. Results: Competent authorities have focused on developing regulatory pathways to address unmet patient needs. Oncology represents the dominating field, followed by cardiovascular, musculoskeletal, neurodegenerative, immunologic, and inherited diseases. Yet, the status remains in early development, and scientific, regulatory, and cost-effectiveness issues impose considerable hurdles toward marketing authorization, technology adoption, and patient accessibility. In this context, although regenerative dentistry has achieved breakthrough innovations in TE of several dental/oral tissues in preclinical models, it has hardly harnessed research progress to integrate innovative regenerative treatments into clinical practice. Conclusion: Global demographic changes, which demonstrate a steady increase of the aging population, highlight the societal need for the application of ATMP-based therapies in the treatment of noncommunicable diseases (NCDs). Although oral diseases, as an integral part of NCDs, are not life-threatening and largely preventable, they sustain high prevalence, with severe burden on economy and quality of life. In this perspective, the urgent request to ultimately translate draining research in dental TE conducted during the last decades into innovative treatments brought safely and cost-effectively into society at large still holds the stage. This review provides an overview of the regulatory, clinical, and commercial status of ATMP-based therapies in the European Union and worldwide and the hurdles to overcome for their broader application in regenerative dentistry.