The technique of cryopreservation (maintenance of biological samples in a state of 'suspended animation' at cryogenic temperatures), its potential use in tissue engineering applications and current obstacles to the development of effective cryopreservation methods for tissues are reviewed. A didactic overview of the principles of cryobiology and the methodology of cryopreservation is given, with emphasis on the processes of injury to cells during freezing and thawing, and how these are related to the physicochemical and biophysical changes occurring during cryopreservation. Critical issues relevant to the application of cryopreservation methods to tissues are then addressed, including heat and mass transfer limitations in these bulk systems, intrinsic differences between isolated and cultured cells, and mechanisms of freezing injury unique to tissue systems.