Clay minerals, recently discovered to be widespread in Mars's Noachian terrains, indicate long-duration interaction between water and rock over 3.7 billion years ago. Analysis of how they formed should indicate what environmental conditions prevailed on early Mars. If clays formed near the surface by weathering, as is common on Earth, their presence would indicate past surface conditions warmer and wetter than at present. However, available data instead indicate substantial Martian clay formation by hydrothermal groundwater circulation and a Noachian rock record dominated by evidence of subsurface waters. Cold, arid conditions with only transient surface water may have characterized Mars's surface for over 4 billion years, since the early-Noachian period, and the longest-duration aqueous, potentially habitable environments may have been in the subsurface.