Ninety nine per cent of all the fresh water on the surface of the Earth is in the form of ice. Observations from space have revealed more about the ice than about most other parts of the environment because at the dawn of the satellite era, less was known about it. The cryosphere includes all forms of naturally occurring ice but here we review what space science has done for knowledge of glaciers and ice sheets. Whereas in global terms the cryosphere exists as a response to climate, over large areas it controls climate. While imaging spacecraft systems have proved easiest to interpret, microwave sensors with poor spatial resolution are able to distinguish transient and stable surface features that are invisible to the eye. Imaging radars quite effectively describe sea ice, but precision altimetry is the only practicable method for monitoring changes in the total mass of ice on land.