Two phenomena which cause damage to cells during cryopreservation are solution effects and intracellular ice formation. Solution effects are caused by concentration of solutes in non-frozen solution during freezing. The mechanism of cell damage due to intracellular ice formation is not well understood.
It is a commonly held misconception that the sharp edges of growing ice crystals cause physical damage to cells when they are freezing, and that this is a mechanism of freezing-related damage. This is incorrect, since crystals do not "move" during crystallisation, but rather add new molecules individually to the surface of the growing crystal. Thus, crystals grow around any solid object in their path.
[Water bear]?s (or tardigrada?), microscopic multicellular organisms, can survive freezing at low temperatures by replacing most of their internal water with the sugar trehalose?.