Antifreeze proteins from polar fish species are remarkable biomacromolecules which prevent the growth of ice crystals. Ice crystal growth is a major problem in cell/tissue cryopreservation for transplantation, transfusion and basic biomedical research, as well as technological applications such as icing of aircraft wings. This review will introduce the rapidly emerging field of synthetic macromolecular (polymer) mimics of antifreeze proteins. Particular focus is placed on designing polymers which have no structural similarities to antifreeze proteins but reproduce the same macroscopic properties, potentially by different molecular-level mechanisms. The application of these polymers to the cryopreservation of donor cells is also introduced.