We report on the results of a survey to document and characterize pedestal craters on Mars equatorward of ∼60°N and 65°S latitude. The identification of 2696 pedestal craters reveals a strong latitude dependence, with the vast majority found poleward of 33°N and 40°S. This latitudinal extent is correlated with many climate indicators consistent with the presence of an ice-rich substrate and with climate model predictions of where ice is deposited during periods of higher obliquity in the Amazonian. We have measured key physical attributes of pedestal craters, including the farthest radial extents of the pedestals, pedestal heights, and the circularity of the pedestal margins. In conjunction with the geographic distribution, our measurements strongly support a sublimation-related formation mechanism. This is in contrast to previous hypotheses, which have relied on eolian deflation to produce the elevated plateaus. The identification of marginal pits on the scarps of some pedestal craters, interpreted to be sublimation pits, provide direct evidence for the presence of ice-rich material underlying the armored surface of pedestal craters. On the basis of our findings, we propose a formation mechanism whereby projectiles impact into a volatile-rich dust/snow/ice substrate tens to hundreds of meters thick overlying a dominantly fragmental silicate regolith. The area surrounding the resulting crater becomes armored. Pedestals extend to a distance of multiple crater radii, farther than typical ejecta deposits, necessitating an armoring mechanism that is capable of indurating the surface to a distance greater than the reach of the ejecta. Return to low obliquity causes sublimation of the volatile-rich layer from the intercrater plains, lowering the elevation of the regional terrain. This yields generally circular pedestal craters elevated above the surrounding plains. As a result, the armored surfaces of pedestal craters have preserved a significant record of Amazonian climate history in the form of ice-rich deposits.