Short answers, pulled from the story.
The Late Heavy Bombardment is hypothesised to have occurred approximately 4.1 to 3.8 billion years ago, corresponding to the Neohadean and Eoarchean eras on Earth. Some researchers argue for a more extended bombardment period lasting from approximately 4.2 to 3.5 billion years ago.
The primary evidence comes from radiometric dating of impact-melt rocks collected during the Apollo 15, 16, and 17 missions. These rocks show a clustering of ages between roughly 3.8 and 4.1 billion years ago, suggesting a concentrated pulse of large impacts. Lunar meteorites and asteroid belt meteorites provide additional supporting data.
The Nice model proposes that the Late Heavy Bombardment resulted from a dynamical instability in the outer Solar System, in which Jupiter and Saturn crossed a 2:1 orbital resonance. This destabilised the orbits of Uranus and Neptune, which scattered objects from the outer belt into the inner Solar System while resonances swept through the asteroid belt, sending many asteroids onto Earth-crossing trajectories.
The bombardment is thought to have sterilised Earth's surface, but computer models developed in May 2009 by a team at the University of Colorado at Boulder suggest that thermophile microbes could have survived in hydrothermal vents below the surface. Manfred Schidlowski argued in 1979 that carbon isotopic ratios in Greenland sedimentary rocks roughly 3.8 billion years old indicate life existed shortly after the bombardment ended.
Two main criticisms exist. First, the clustering of impact-melt ages near 3.9 billion years ago may reflect ejecta from a single large impact, the Imbrium basin, rather than multiple independent events. Second, the absence of impact-melt rocks older than about 4.1 billion years may be because older samples were pulverised or had their radiometric ages reset by continuous cratering, not because fewer impacts occurred.
The Planet V hypothesis proposes that a fifth terrestrial planet with a mass less than half that of Mars originally orbited between Mars and the asteroid belt. Perturbations from the other inner planets drove its orbit into the inner asteroid belt, destabilising many asteroids and directing them onto Earth-crossing paths. Planet V was ultimately lost, most likely by falling into the Sun.