The preservative effects of low temperature on biological materials have been long recognised, and cryopreservation is now widely used in biomedicine, including in organ transplantation, regenerative medicine and drug discovery. The lack of organs for transplantation constitutes a major medical challenge, stemming largely from the inability to preserve donated organs until a suitable recipient is found. Here, we review the latest cryopreservation methods and applications. We describe the main challenges-scaling up to large volumes and complex tissues, preventing ice formation and mitigating cryoprotectant toxicity-discuss advantages and disadvantages of current methods and outline prospects for the future of the field.