Although sperm were successfully cryopreserved in 1950, another 22 years elapsed before the successful preservation of a mammalian embryo. In 1963, I had carried out physical–chemical analyses indicating that if cells were cooled too rapidly, they would undergo lethal intracellular ice formation (IIF), and defined what is meant by “too rapidly” for a particular cell. To avoid IIF, the cell had to dehydrate during cooling, and the required rate of cooling depended chiefly on the permeability of a particular cell to water and on the temperature coefficient of that permeability. Between 1968 and 1972, Stanley Leibo and I turned our attention to the survival of yeast, mouse marrow stem cells, and Chinese Hamster tissue culture cells as functions of cooling rate and temperature. We found that plots of survival vs. cooling rate formed an inverted “U”, with high survivals at a medium rate, and lower survivals after very slow and very rapid cooling. We proposed a “Two-Factor” hypothesis which stated that the right hand arm of the inverted U was a result of IIF at high cooling rates. Interestingly, the optimum cooling rate for maximum survival varied over a wide range for the different cells. This was chiefly because the cells differed widely in water permeability and the temperature coefficient of that permeability. In fact if the known values of these parameters were used to generate the theoretical curves, the predicted relation between IIF and cooling rate agreed quite closely with the observed drop in survival vs. cooling rate. In 1971 David Whittingham reported the successful cryopreservation of mouse 8-cell embryos cooled at 50 °C/min in PVP. Leibo and I were excited but perplexed about these results – perplexed because our computations indicated that mouse embryos would undergo lethal IIF when cooled at that rate. We calculated that the cooling rate would have to be about 1 °C/min.. That turned out to be the case. With that change and the substitution of Me 2 SO for PVP, David, Stanley and I obtained very good in vitro and in vivo survival of 8-cell embryos cooled to −196 °C (or −269 °C). The ability to cryopreserve mouse embryos quickly had important applied consequences and important fundamental consequences. Perhaps, the most important direct application was that it permitted the long-term maintenance of thousands of mutant lines of mice in the form of preimplantation embryos in a few liquid nitrogen tanks. The indirect applications stemmed from the fact that essentially the same procedures worked for early embryos of over 20 other mammals, including humans. In the last decade, clinical interest has been emphasizing the cryopreservation of human oocytes. They have proved more difficult to freeze and so interest has shifted somewhat to cryopreserving them by vitrification. As discussed, one way to avoid lethal IIF is to cool cells slowly enough so that the freezable water in the cell flows out of the cell and freezes externally. An alternative approach is to avoid intracellular ice by vitrifying cellular water. Vitrification involves converting water into a non-crystalline or amorphous glass. To achieve this conversion, it has been the strong belief that cells have to be in solutions containing a very high concentration of glass-inducing solutes and have to be cooled very rapidly. In recent work, however, we have found that neither of these is true for mouse oocytes. The important factor is not the cooling rate – it is the warming rate, and the warming rate has to be very high. Furthermore, if the warming rate is very high, one can cut in half the concentration of solutes in the vitrification solution and still obtain high survivals.