The Neoproterozoic is a time of transition between the ancient microbial world and the Phanerozoic, marked by a resumption of extreme carbon isotope fluctuations and glaciation after a billion-year absence. The carbon cycle disruptions are probably accompanied by changes in the stock of oxidants and connect to glaciations via changes in the atmospheric greenhouse gas content. Two of the glaciations reach low latitudes and may have been Snowball events with near-global ice cover. This review deals primarily with the Cryogenian portion of the Neoproterozoic, during which these glaciations occurred. The initiation and deglaciation of Snowball states are discussed in light of a suite of general circulation model simulations designed to facilitate intercomparison between different models. Snow cover and the nature of the frozen surface emerge as key factors governing initiation and deglaciation. The most comprehensive model discussed confirms the possibility of initiating a Snowball event with a plausible reduction of CO2. Deglaciation requires a combination of elevated CO2 and tropical dust accumulation, aided by some cloud warming. The cause of Neoproterozoic biogeochemical turbulence, and its precise connection with Snowball glaciations, remains obscure.