The Cryonics Insitute, founded in 1976, is one of two major cryonics organizations in the United States that cryopreserves people upon their legal deaths. You can find more about them on their about page.

A classic critique of cryonics is that the organizations may face bankruptcy, and be forced to thaw their patients. In fact,

Early attempts at cryonics facilities have previously failed when the organisations went bankrupt. Several facilities existed in the US starting in the 1960s, which often relied on funding from the living relatives of the cryopreserved, and could not maintain conditions when relatives were no longer willing or able to pay. As a result, all but one of the documented cryonic preservations prior to 1973 ended in failure, and the thawing out and disposal of the bodies.

You can find more specific information about the history of brain preservation on this page by Metaculite Mati Roy.

Jeff Kaufman maintains a spreadsheet of cryonics probability estimates, which you can find on this page.

See also this question for Alcor.