The Neoproterozoic contains severe glacial intervals (750-580 Ma) including two extending to low palaeomagnetic latitudes. Paucity of radiometric dates indicates the need for chronostratigraphic tools. Whereas the marine 87Sr/86Sr signatures show a steady rise, δ13C fluctuates, the most reproducible variations being negative signatures in carbonate caps to glacial units, but more diagenetic work is needed. Four conceptual models for the icehouse conditions are contrasted: Zipper-Rift Earth (diachronous glaciation related to continental rift margins), High-tilt Earth (high-obliquity and preferential low-latitude glaciation), Snowball Earth (extreme glaciation related to runaway ice-albedo feedback) and Slushball Earth (coexistence of unfrozen oceans and sea-level glaciers in the tropics). Climate models readily simulate runaway glaciation, but the Earth may not be able to recover from it. The Slushball state requires more extensive modelling. Biogeochemical models highlight the lack of CO2 buffering in the Neoproterozoic and the likely transition from a methane- to a CO2-dominated climate system. Relevant processes include tropical weathering of volcanic provinces, and new land biotas stimulating both clay mineral formation and P delivery to the oceans, facilitating organic C burial. Hence a step change in the Earth System was probably both facilitated by organisms and responsible for moderating Phanerozoic climate.