We know about this late heavy bombardment (LHB)
from dating lunar surfaces. How do we date lunar
surfaces?
http://www.lpl.arizona.edu/SIC/impact_cratering/lunar_cataclysm/Lunar_Cataclysm_Page
One big controversy about the idea of the LHB -- and there are many
controversies -- is that it is essentially impossible for us ever
to figure out if the Earth also had a LHB. We are only able to
extrapolate from the Moon. Do you know why we can't figure it out
directly for the Earth?