Here we make the first quantitative estimates of the maximum total number of large terrestrial impact craters that can survive until the current era on Earth. Our estimates of crater survival are made using the age of Earth’s crust and the expected flux of large extraterrestrial bodies striking Earth. This analysis neglects effects such as weathering and burial, which tend to preferentially erase smaller craters. Thus, our results represent the maximum number of craters we expect to exist on Earth today. Although the constant recycling of crustal material creates a strong bias toward younger ages, our model suggests that the terrestrial cratering record can be used to determine the size frequency distribution of the impactors that bombarded Earth over the past 3.5 G.y. However, our model suggests that the cratering record cannot be used to distinguish between scenarios with a constant flux of impactors over time and scenarios where the bombardment rate was considerably higher in Earth’s ancient history. Luckily, layers of distal impact ejecta may act as records of impacts even when the source craters have been tectonically recycled. We suggest that searches for these distal impact ejecta layers will be more fruitful for constraining the bombardment history of Earth than searches for large craters.