Large flood channels, valley networks and a variety of features attributed to the action of ground ice indicate that Mars emerged from heavy bombardment 3.8 Ga ago, with an inventory of water at the surface equivalent to at least a few hundred metres spread over the whole planet, as compared with 3 km for the Earth. The mantle of Mars is much drier than that of the Earth, possibly as a result of global melting at the end of accretion and the lack of plate tectonics to subsequently reintroduce water into the interior. The surface water resided primarily in a porous, kilometres-thick megaregolith created by the high impact rates. Under today's climatic conditions groundwater is trapped below a thick permafrost zone. At the end of heavy bombardment any permafrost zone would have been much thinner because of the high heat flows, but climatic conditions may have been very different then, as suggested by erosion rates 1000 times higher than subsequent rates. Water trapped below the permafrost periodically erupted onto the surface to form large flood channels and lakes. Given abundant water at the surface and sustained volcanism, hydrothermal activity must have frequently occurred but we have yet to make the appropriate observations to detect the results of such activity.