Cryopreservation is a process that preserves organelles, cells, tissues, or any other biological constructs by cooling the samples to very low temperatures. The responses of living cells to ice formation are of theoretical interest and practical relevance. Stem cells and other viable tissues, which have great potential for use in basic research as well as for many medical applications, cannot be stored with simple cooling or freezing for a long time because ice crystal formation, osmotic shock, and membrane damage during freezing and thawing will cause cell death. The successful cryopreservation of cells and tissues has been gradually increasing in recent years, with the use of cryoprotective agents and temperature control equipment. Continuous understanding of the physical and chemical properties that occur in the freezing and thawing cycle will be necessary for the successful cryopreservation of cells or tissues and their clinical applications. In this review, we briefly address representative cryopreservation processes, such as slow freezing and vitrification, and the available cryoprotective agents. In addition, some adverse effects of cryopreservation are mentioned.