The idea of stasis has been with us in fiction for hundreds of years now. According to the Encyclopedia of Science Fiction, LS Mercier made references in pre-Revolutionary France. The idea of time travel through suspended animation is something I realize I take for granted. I read a TON of sci-fi as a kid so I encountered the concept often. I don't think I ever thought it could be possible in my lifetime.
A rabbit's brain has been more or less successfully preserved: http://www.scientificamerican.com/article/can-our-minds-live-forever/
The technique does not preserve future biological viability but allows for detailed scanning and preservation of the "connectome" which would theoretically allow synthetic reproduction at a future date when technology exists. It would potentially make possible "nanometer-scale scanning of the preserved brain to serve as basis for mind uploading." Synthetic revival in the future! That is actually a step beyond most of the sci-fi scenarios.
The next step is a large mammal brain - a pig. Robert McIntyre, the lead researcher, has already started a company called Nectome to potentially adapt the process to terminal patients in a hospital setting.