Cryopreservation is a unique and practical method to facilitate extended access to biological materials. Because of this, cryopreservation of cells, tissues, and organs is essential to modern medical science, including cancer cell therapy, tissue engineering, transplantation, reproductive technologies, and bio-banking. Among diverse cryopreservation methods, significant focus has been placed on vitrification due to low cost and reduced protocol time. However, several factors, including the intracellular ice formation that is suppressed in the conventional cryopreservation method, restrict the achievement of this method. To enhance the viability and functionality of biological samples after storage, a large number of cryoprotocols and cryodevices have been developed and studied. Recently, new technologies have been investigated by considering the physical and thermodynamic aspects of cryopreservation in heat and mass transfer. In this review, we first present an overview of the physiochemical aspects of freezing in cryopreservation. Secondly, we present and catalog classical and novel approaches that seek to capitalize on these physicochemical effects. We conclude with the perspective that interdisciplinary studies provide pieces of the cryopreservation puzzle to achieve sustainability in the biospecimen supply chain.