Modeling facilitates understanding of the biophysical and some of the biochemical mechanisms of damage during all phases of cryopreservation including CPA equilibration and cooling and warming. Moreover, as a tool for optimization of cryopreservation protocols, modeling has yielded many successes. Modern cryobiological modeling includes very detailed descriptions of the physical phenomena that occur during freezing, including ice growth kinetics and spatial gradients that define heat and mass transport models.