It may seem like a trendy way to be put to rest in the 1970s that sounded awesome, feasible, and totally scifi at the time, but the practice of freezing a whole body or just a head/brain is still in practice today. These hopeful people feel they are making the best decision possible to be brought back from death's grip some time in the future when technology can revive them from both death and freezing....
What makes people believe someone can be brought back from a frozen state? Well, such a thing, under the right conditions has occurred in nature.
Justin Smith was a man who had been left out by the roadside in a drunken state on a cold night. He was found the next day, frozen, blue, and completely lifeless. Using emergency techniques for extreme hypothermia, it was attempted to bring him back.
They gave it a chance at the hospital and ran his blood through a machine that would slowly warm him and get blood moving and oxygen as well. Before they knew it, his heart was beating again.
They worried about his brain function, as most people with oxygen deprivation for more than several minutes can have anoxic brain injury. In this case, lowering his body temperature was done in such a way outdoors that it slowed functions down and they were able to come back "online" when he was warmed. (LINK to more on this case)
This very reality is what sparks the cryogenics movement. There are critics of such an idea. In the first case, Justin was alive when he underwent freezing. That is different than someone who dies of, say, cancer and they put them into cryogenic freeze. Functions ideally should be running when you freeze the person down. Bringing back someone who was dead upon freezing is wishful thinking. The hope for some is that, much further down the line, bringing people back from death is not so odd.
LINK: If a person is cooled below -5C the water inside their cells freezes and creates ice crystals. As ice is less dense than liquid water, it takes up more space. So the crystals punch through the cell membranes causing severe damage.
If we take an ice cube as an example, in one case, you fill an ice cube tray and leave it in the freezer. An hour later, you might go to get an ice cube and find it has a hard layer on the outside, but it still liquid inside. Leave it in the freezer too long and it's solid. There is a question about the concept of superfreezing people and getting anything viable from thawing.
No one has ever revived someone who was vitrified/fully frozen.
The movie, "Iceman" was a fantastical concept of a caveman who got frozen and was thawed out. How does he handle life here? How do we handle him? Imagine being a Rumpelstiltskin and waking up after tens of thousands of years? If we were to put down into a cold stasis, would we awaken to a world that we are not adapted to? Perhaps the air is very polluted and we did not evolve to handle it. Perhaps customs and roles have changed. Maybe we even awaken to become a slave to a greater being....
Detailed documentation of a freezing process of a Hollywood professional (LINK).
Alcor Life Extension Foundation (LINK).