River valleys and deposits record periods of time when Mars’ climate supported liquid water on the planet’s surface. However, the majority of geomorphic studies focus on detailed reconstructions of local or regional hydrology, thereby limiting our global understanding of Mars’ climate through time. In this dissertation, we set out to constrain our view of Mars’ climate history through novel applications of impact crater statistics. Impact craters are ideal for probing the history of river erosion because (a) they formed globally throughout history and (b) they record geologic and solar system processes in their morphologies and populations. In Chapter 2, we tested the hypothesis that ancient Martian surfaces were subjected to intense resurfacing by river erosion. Using statistical methods developed by astronomers to detect galactic clustering on the celestial sphere, we found that resurfacing on the ancient Martian highlands was shallower than previously expected. In Chapter 3, we investigated the duration of chaotic high-obliquity excursions, which are believed to have enabled river-forming climates in the last ~3.5 Gyr. Using a novel model relating Mars’ obliquity to the distribution of elliptic impact crater orientations, we found that the amount of time Mars spent in a high obliquity state was ~50% lower than expected. In Chapter 4, we used global databases of impact craters and alluvial fans to constrain parameters in a statistical model for global fan formation. We found that climate-driven alluvial fan formation likely persisted into the last ~2.5 Gyr. In Chapter 5, we synthesized our work and described how our observations together directionally affect our view of Mars’ climate evolution. In the supplementary files, we include minor planet center and elliptic crater data.