Geomorphological, mineralogical and other evidence of the conditions favoring the existence of water on Mars in liquid phase is reviewed. This includes signatures of past and, possibly, present aqueous environments, such as the northern ocean, lacustrine environments, sedimentary and thermokarst landforms, glacial activity and water erosion features. Reviewed also are hydrous weathering processes, observed on surface remotely and also via analysis of Martian meteorites. Chemistry of Martian water is discussed: the triple point, salts and brines, as well as undercooled liquid interfacial and solid-state greenhouse effect melted waters that may still be present on Mars. Current understanding of the evolution of Martian hydrosphere over geological timescales is presented from early period to the present time, along with the discussion of alternative interpretations and possibilities of dry and wet Mars extremes.