Valvular heart disease is a major cause of morbidity and mortality worldwide. Surgical valve repair or replacement has been the standard of care for patients with valvular heart disease for many decades, but transcatheter heart valve therapy has revolutionized the field in the past 15 years. However, despite the tremendous technical evolution of transcatheter heart valves, to date, the clinically available heart valve prostheses for surgical and transcatheter replacement have considerable limitations. The design of next-generation tissue-engineered heart valves (TEHVs) with repair, remodelling and regenerative capacity can address these limitations, and TEHVs could become a promising therapeutic alternative for patients with valvular disease. In this Review, we present a comprehensive overview of current clinically adopted heart valve replacement options, with a focus on transcatheter prostheses. We discuss the various concepts of heart valve tissue engineering underlying the design of next-generation TEHVs, focusing on off-the-shelf technologies. We also summarize the latest preclinical and clinical evidence for the use of these TEHVs and describe the current scientific, regulatory and clinical challenges associated with the safe and broad clinical translation of this technology.