Cryopreserved human heart valves fill a crucial role in the treatment for congenital cardiac anomalies, since the use of alternative mechanical and xenogeneic tissue valves have historically been limited in babies. Heart valve models have been used since 1998 to better understand the impact of cryopreservation variables on the heart valve tissue components with the ultimate goals of improving cryopreserved tissue outcomes and potentially extrapolating results with tissues to organs. Cryopreservation traditionally relies on conventional freezing, employing cryoprotective agents, and slow cooling to sub-zero centigrade temperatures; but it is plagued by the formation of ice crystals and cell damage upon thawing. Researchers have identified ice-free vitrification procedures and developed a new rapid warming method termed nanowarming. Nanowarming is an emerging method that utilizes targeted application of energy at the nanoscale level to rapidly rewarm vitrified tissues, such as heart valves, uniformly for transplantation. Vitrification and nanowarming methods hold great promise for surgery, enabling the storage and transplantation of tissues for various applications, including tissue repair and replacement. These innovations have the potential to revolutionize complex tissue and organ transplantation, including partial heart transplantation. Banking these grafts addresses organ scarcity by extending preservation duration while preserving biological activity with maintenance of structural fidelity. While ice-free vitrification and nanowarming show remarkable potential, they are still in early development. Further interdisciplinary research must be dedicated to exploring the remaining challenges that include scalability, optimizing cryoprotectant solutions, and ensuring long-term viability upon rewarming in vitro and in vivo.