We've been using the art of cryopreservation or cell freezing for decades. The main problem with this technique is how to prevent ice crystals from forming inside the cells. These crystals have sharp edges that can cause damage to delicate cell structures. It's also true that freezing as a method of preservation always causes some deterioration in the quality of the item frozen. Think of the difference between fresh and frozen chicken, for example. Chicken that has been frozen is tougher, less juicy, and not as flavorful.
This difference in quality can be attributed to cell death. The freezing and thawing processes alter the structure of the items in question. Some scientists have voiced skepticism about the cryopreservation of large organs or body parts as a result of this type of cell death and subsequent deterioration of the items in question. The difference between the cryopreservation of organs and body parts, or eggs, embryos, and sperm is related to the small size of the latter group, which makes them more amenable to the freezing and thawing processes.
Embryos considered for cryopreservation are blastocysts and contain 100-120 cells. Because there are fewer cells in say, a sperm, than in an organ, such as a liver, which may contain billions of cells, the freeze/thaw process is less involved and more conducive to success without so much attendant cell death.
It is believed that embryos can be stored for as long as 14 years without sustaining significant degradation. But most people don't wait as long as 14 years to have another baby. That's a good thing, since the longer the embryos are stored, the more vulnerable they are to deterioration.
As for the thawing process, the main worry is in rehydrating the cell without causing it to explode. The embryos, sperm, or eggs are warmed with air and in water baths rather than in a machine. The system is not precise and is slower than the cooling time, which takes about 2 hours.
Embryos can be implanted two-four hours after reaching body temperature. Sperm are the easiest to freeze and thaw since they contain no cytoplasm and are therefore not susceptible to cell damage.
The first live birth resulting from a cryopreserved embryo occurred in 1986. The birth rate for IVF with frozen embryos is two thirds that of the same procedure performed with fresh embryos. However, it's important to factor in a woman's age at the time a frozen embryo would have been implanted, since it is an older woman who is liable to use a cryopreserved and thawed embryo in this process.