A range of cold desert landforms are found on the Martian surface that have been interpreted to indicate prevailing frozen and hyperarid conditions for at least the past several million years. These cold desert conditions are punctuated by brief periods of localized surficial liquid water flow. Sediment transport pathways operate under these conditions of extreme cold and aridity and the processes involved generate permafrost landforms that are recognizable from spacecraft at local, regional and global scales. Thermal-contraction-crack polygons are associated with hemisphere-spanning mantle units that contain excess ice in the immediate subsurface. Sublimation is the dominant phase transition rather than melting under present Martian conditions. Evidence is presented for melting of near-surface snow, frost and/or ground ice in protected gully alcove microclimates during the most recent several million years.