To model the cryobiological responses of cells and tissues, the cellular membrane permeability characteristics are often measured at suprazero temperatures as well as at subzero temperatures with and without the presence of extra-cellular ice. These measured membrane permeability characteristics are then used to predict the responses of cells and tissues for a given thermal insult with the ultimate aim of mitigating the damage caused during the freeze-thaw process. This brief review articles summarizes efforts from my research group over the past 15 years as related to cryobiology of mammalian ovarian tissue sections, i.e., the known knowns as well as the critical cryobiological knowledge that is still lacking to rationally design optimal cryopreservation protocols for ovarian tissues, i.e., the known unknowns.