While valley networks seem to attest to the fact that liquid water existed on Mars during a "climatic optimum," modified impact craters attest to the fact that some form of precipitation and surface runoff occurred throughout the entire early history of Mars. Modified impact craters have been heavily eroded. Because they are preserved at a range of sizes and stages of modification, they indicate that erosion was a long-lived process that continued as new craters were forming. Unlike valley networks, they are also found practically everywhere on Mars in the older terrain, suggesting that the process that modified them was global. We are in the process of conducting a systematic analyses of all modified impact craters on Mars to determine how much erosion they represent, what types of geologic processes best describe their shapes, and whether there are any regional differences in the amount of erosion and the modification processes.