Millions of human oocytes and embryos are stored in thousands of locations across the globe. This inventory continues to grow as cryopreservation becomes more successful and more widely applied. The results of studies assessing pregnancy and neonatal outcomes following frozen embryo transfer (FET) have been encouraging, showing lower incidences of small for gestational age neonates and preterm birth compared with fresh transfers. However, many of these studies have also shown that the odds of large for gestational age births and macrosomia are higher after FET. The origin of these conditions remains unclear. Cryostorage presents many potential risks to the cryopreserved cells/tissues, including loss of viability and contamination, but risks are faced also by care providers—for example, injury and financial liability—and by patients—for example, accidental loss of their reproductive tissues, the burden of embryos they no longer wish to use and failing to meet their contractual obligations. Studies are urgently needed to explore and understand all dimensions of cryostorage to help ART clinics develop effective strategies to manage associated risks. The future of cryostorage, as for many other areas of ART and medicine, is automation.