Transporting tissues and organs from the site of donation to the patient in need, while maintaining viability, is a limiting factor in transplantation medicine. One way in which the supply chain of organs for transplantation can be improved is to discover novel approaches and technologies that preserve the health of organs outside of the body. The dominant technologies that are currently in use in the supply chain for biological materials maintain tissue temperatures ranging from a controlled room temperature (+25 °C to +15 °C) to cryogenic (−120 °C to −196 °C) temperatures (reviewed in Criswell et al. Stem Cells Transl Med. 2022). However, there are many cells and tissues, as well as all major organs, that respond less robustly to preservation attempts, particularly when there is a need for transport over long distances that require more time. In this perspective article, we will highlight the current challenges and advances in biopreservation aimed at “freezing biological time,” and discuss the future directions and requirements needed in the field.