We have constructed a model that predicts the evolution of CO2 on Mars from the end of the heavy bombardment period to the present. The model draws on published estimates of the main processes believed to affect the fate of CO2 during this period: chemical weathering, regolith uptake, polar cap formation, and atmospheric escape. Except for escape, the rate at which these processes act is controlled by surface temperatures which we calculate using a modified version of the Gierasch and Toon energy balance model (1973, J. Atmos. Sci. 30, 1502-1508). The modifications account for the change in solar luminosity with time, the greenhouse effect, and a polar and equatorial energy budget.Using published estimates for the main parameters, we find no evolutionary scenario in which CO2 is capable of producing a warm (global mean temperatures >250 K) and wet (surface pressures >30 mbar) early climate, and then evolves to present conditions with ∼7 mbar in the atmosphere, <300 mbar in the regolith, and <5 mbar in the caps. Such scenarios would only exist if the early sun were brighter than standard solar models suggest, if greenhouse gases other than CO2 were present in the early atmosphere, or if the polar albedo were significantly lower than 0.75. However, these scenarios generally require the storage of large amounts of CO2 (>1 bar) in the carbonate reservoir. If the warm and wet early Mars constraint is relaxed, then we find best overall agreement with present day reservoirs for initial CO2 inventories of 0.5-1.0 bar. We also find that the polar caps can have a profound effect on how the system evolves. If the initial amount of CO2 is less than some critical value, then there is not enough heating of the poles to prevent permanent caps from forming. Once formed, these caps control how the system evolves, because they set the surface pressure and, hence, the thermal environment. If the initial amount of CO2 is greater than this critical value, then caps do not form initially, but can form later on, when weathering and escape lower the surface pressure to a point at which polar heating is no longer sufficient to prevent cap formation and the collapse of the climate system. Our modeling suggests this critical initial amount of CO2 is between 1 and 2 bar, but its true value will depend on all factors affecting the polar heat budget.