Preservation of female genetics is currently done primarily by means of oocyte and embryo cryopreservation. The field has seen much progress during its four-decade history, progress driven predominantly by research in humans, cows, and mice. Two basic cryopreservation techniques rule the field -controlled-rate freezing, the first to be developed, and vitrification, which, in recent years, has gained a foothold. While much progress has been achieved in human medicine, the cattle industry, and in laboratory animals, this is far from being the case for most other mammals and even less so for other vertebrates. The major strides and obstacles in human and other vertebrate oocyte and embryo cryopreservation will be reviewed here.