We explore the role of large impacts in creating the Martian valley networks. Recent dating shows that some large impact basins are contemporaneous with the valley networks. The mass deposited (and volatiles released) by impacts is large, and comparable with the mass from the Tharsis volcanic construct. Steam atmospheres formed after large impacts can produce more than 600 m of rainfall, followed by rainfall from water-vapor greenhouse atmospheres, and snowmelt. The erosion rates from impacts that created the currently visible craters are somewhat less than the erosion rates suggested for the Noachian (4.2 to 3.82 Gya). There are several possible explanations for this difference, and it is possible that erosion rates are overestimated because the burial of small craters by global debris layers from impacts has not been considered. Rainfall after the Noachian was low because the impact rate and CO2 pressure declined. We suggest tests of the hypothesis that impacts caused the river valleys.