Impact events that produce large craters primarily occurred early in the Solar System's history because the largest bolides were remnants from planetary formation. Determining when large impacts occurred on a planetary surface such as Mars can yield clues to the flux of material in the early inner Solar System which, in turn, can constrain other planetary processes such as the timing and magnitude of resurfacing and the history of the martian core dynamo. We have used a large, global planetary database in conjunction with geomorphologic mapping to identify craters superposed on the rims of 78 larger craters with diameters D ⩾ 150 km on Mars, ≈78% of which have not been previously dated in this manner. The densities of superposed craters with diameters larger than 10, 16, 25, and 50 km, as well as isochron fits were used to derive model crater ages of these larger craters and basins from which we derived an impact flux. In discussing these ages, we point out several internal inconsistencies of crater-age modeling techniques and chronology systems and, all told, we explain why we think isochron-fitting is the most reliable indicator of an age. Our results point to a mostly obliterated crater record prior to ∼4.0 Ga with the oldest preserved mappable craters on Mars dating to ∼4.3-4.35 Ga. We have used our results to constrain the cessation time of the martian core dynamo which we found to have occurred between the formation of Ladon and Prometheus basins, approximately 4.06-4.09 Ga. We also show that, overall, surfaces on Mars older than ∼4.0-4.1 Ga have experienced >1 km of resurfacing, while those younger than ∼3.8-3.9 Ga have experienced significantly less.