Relief inversion has been invoked to explain a number of geomorphic features of the martian surface. Terrestrial relief inversion occurs when former depressions become elevated because their fill is more resistant to erosion than the surrounding terrain. It is a common product of long-term landscape evolution on Earth, especially in relatively stable intra-cratonic settings and flat, or near flat lying successions. The inverted relief will preserve relicts of former land surfaces and is therefore older than the surrounding terrain. Relief inversion can occur by a range of processes, including infill of depressions by intrinsically resistant material, selective secondary cementation via diagenesis and weathering, or surface armouring. We examine a number of possible cases of inverted relief on Mars that appear to have formed by these three processes. We suggest that the most likely cementing agents for surface induration are iron oxides, silica, and sulfates. Possible cementation mechanisms include fluid mixing during regional groundwater flow, cooling of hydrothermal or basinal fluids as they near the surface, and evaporation and sublimation of near surface water. Wind action appears the most common erosive process on Mars capable of the regional landscape lowering necessary for relief inversion to occur, unlike on Earth where both deflation and runoff are important. Preliminary crater densities of selected features show that the tops of the proposed inverted relief have considerably more craters than the surrounding plains, as is predicted by the inversion hypothesis. More accurate dating of inverted surfaces and the adjacent areas may provide a simple way of measuring the degree of erosion over time in at least some areas of Mars.