Numerous landforms with traits that are suggestive of formation by periglacial processes have been observed in Utopia Planitia, Mars. They include: small-sized polygons, flat-floored depressions, and polygon trough or junction pits. Most workers agree that these landforms are late Amazonian and mark the occurrence of near-surface regolith that is (was) ice rich. The evolution of the Martian landforms has been explained principally by two disparate hypotheses. The first is the “wet hypothesis.” It is derived from the boundary conditions and ice-rich landscape of regions such as the Tuktoyaktuk Coastlands, Canada, where stable liquid water is freely available as an agent of landscape modification. The second is the “dry” hypothesis. It is adapted from the boundary conditions and landscape-modification processes in the glacial Dry Valleys of the Antarctic, where mean temperatures are much colder than in the Tuktoyaktuk Coastlands, liquid water at or near the surface is rare, and sublimation is the principal agent of glacial mass loss. Here, we (1) describe the ice-rich landscape of the Tuktoyaktuk Coastlands and their principal periglacial features; (2) show that these features constitute a coherent assemblage produced by thaw-freeze cycles; (3) describe the landforms of Utopia Planitia and evaluate the extent to which “wet” or “dry” periglacial processes could have contributed to their formation; and (4) suggest that even if questions concerning the “wet” or “dry” origin of the Martian landforms remain open, “dry” processes are incapable of explaining the origin of the ice-rich regolith itself, from which the landforms evolved.