Cryopreservation describes techniques that permit freezing and subsequent warming of biological samples without loss of viability. The application of cryopreservation in assisted reproductive technology encompasses the freezing of gametes, embryos, and primordial germ cells. Whilst some protocols still rely on slow-freezing techniques, most now use vitrification, or ultra-rapid freezing, for both oocytes and embryos due to an associated decreased risk of damage caused by the lack of ice crystal formation, unlike in slow-freezing techniques. Vitrification has demonstrated its use in many applications, not only following IVF procedures in human embryology clinics but also following in vitro production of embryos in agriculturally important, or endangered animal species, before embryo transfer. Here, we review the various cryopreservation and vitrification technologies that are used in both humans and other animals and discuss the most recent innovations in vitrification with a particular emphasis on their applicability to animal embryology.