For decades, scientists have looked for the causes of cell cryoinjury so as to identify the optimum conditions for freezing and storing frozen cells. Cell dehydration and intracellular ice formation have been argued as the main mechanisms of cell damage. Maintaining the cells in a vitreous matrix below the glass transition temperature of the surrounding medium is known as a key condition for cell preservation. However, it is only in 2013 that the measurement of the intracellular glass transition of different cell types has been made possible. Moreover, the relevance of intracellular and extracellular vitrification during slow cooling of microorganisms and mammalian cells has been the subject of recent research. The physical events taking place during freezing are reviewed here, focusing on the role of the physical state of the intracellular and extracellular environments in determining the response of cells to stresses encountered during cryopreservation. The implications on cryoprotectants selection, freezing rates, and controlled cooling endpoint to be set for cell storage are discussed.