The incidence of severe valvular dysfunctions (e.g., stenosis and insufficiency) is increasing, leading to over 300,000 valves implanted worldwide yearly. Clinically used heart valve replacements lack the capacity to grow, inherently requiring repetitive and high-risk surgical interventions during childhood. The aim of this review is to present how different tissue engineering strategies can overcome these limitations, providing innovative valve replacements that proved to be able to integrate and remodel in pre-clinical experiments and to have promising results in clinical studies. Upon description of the different types of heart valve tissue engineering (e.g., in vitro, in situ, in vivo, and the pre-seeding approach) we focus on the clinical translation of this technology. In particular, we will deepen the many technical, clinical, and regulatory aspects that need to be solved to endure the clinical adaptation and the commercialization of these promising regenerative valves.