I'm curious as to how freezing fertilized eggs/embryos, doesn't kill them? when if we froze our bodies our cells would die.

Cryopreservatives: Techniques for freezing eggs or any cells exist and allow scientists to preserve and study many different types of cells.This is particularly useful in studying cancer cells.Techniques have been developed with special chemicals that allow the cells to be frozen without rupture of the cell membranes(water expands when frozen). The cells are stored indefinitely in liquid nitrogen.

Good question!: Eggs and embryos seem to do best with a process called vitrification which causes such a dramatic and rapid plunge in temperature that ice crystals do not form. This allows preservation of delicate cellular structures. The frozen or vitrified eggs and embryos are stored at such a low temperature that the molecules supposedly do not really move. So no "freezer burn"!

Egg freezing: Egg an embryo freezing is done for a single cell (egg) or several cells (embryo) with conditions of freezing optimized for each. However, freezing organs is more difficult as conditions are not as controlled when dealing with different cells each having different requirements. You can see how an entire body becomes even more difficult.