Surface conditions on Mars are currently cold and dry, with water ice unstable on the surface (except near the poles) and no liquid water. However, recent glacier-like landforms have been identified in the tropics and mid-latitudes of Mars, an ice-rich mantling seems to cover both hemisphere above 60°lat., and recent gullies apparently carved by liquid-water are observed. To better understand the processes that have formed such features, we have performed high resolution climate simulations with a numerical model designed to simulate the details of the present-day Mars water cycle, but using different obliquities, like on Mars in the past. At high obliquity (e.g. 45°), the model predicts the accumulation of ice and the formation of glaciers on the western flanks of the great Tharsis volcanoes if the current northern polar cap remains a source of water, and in eastern Hellas if a water ice polar cap is assumed to be present at the southern pole. This is precisely where the most characteristic Glacier-like features have been discovered. The agreement between observed glacier landform locations and model predictions points to an atmospheric origin for the ice and permits a better understanding of the details of the formation of Martian glaciers. Using the same model, we show that when Mars returns to lower obliquity, the low and mid-latitude glaciers becomes unstable, partially sublimes and ice tends to accumulate in both hemisphere above 60°. Once water is no more available from the low and mid-latitude, it tends to return to the poles (where it is now), but some ice is probably left under a dry layer. As suggested by previous studies, this would explain the presence of the ice-rich mantling observed on the surface and detected by GRS aboard Mars Odyssey. In this scenario, the formation of glaciers and ice layers on Mars is the product of the same Martian climate system as that of today, except that the enhanced water cycle allows the precipitation and accumulation of ice in specific locations controlled by the atmospheric circulation. In reality, the complex variations of orbital parameters probably led to all sorts of regimes in the past, with water ice alternatively mobilized from the poles to the tropical and mid-latitude glaciers and to the high latitudes. After several obliquity cycle, this processes could have created layers that could be detected by Phoenix in 2008. Moreover, on the basis of the ice accumulation and loss rates that are modeled at the north pole, we can try to reconstruct the history of the ice accumulation there in the past 10 millions years and compare the modeled layers with the ones observed in the polar deposits throughs. It is also likely that some of the past Mars Climate regimes led to the accumulation of ice on slopes that could have had reached the melting point of water and initiate debris flows and Gullies, in some specific conditions that we can investigate with the climate models. Overall, we can thus propose a simple, consistent scenario to explain the formation many of the amazonian icy landforms by the climate system that we know today, without the involvement of subsurface reservoir.