New data on lunar craters and recent discoveries about craters on Earth permit a reassessment of the bombardment history of Earth over the last 3.2 billion years. The combined lunar and terrestrial crater records suggest that the long-term average rate of production of craters larger than 20 km in diameter has increased, perhaps by as much as 60%, in the last 100 to 200 million years. Production of craters larger than 70 km in diameter may have increased, in the same time interval, by a factor of five or more over the average for the preceding three billion years. A large increase in the flux of long-period comets appears to be the most likely explanation for such a long-term increase in the cratering rate. Two large craters, in particular, appear to be associated with a comet shower that occurred about 35.5 million years ago. The infall of cosmic dust, as traced by 3He in deep sea sediments, and the ages of large craters, impact glass horizons, and other stratigraphic markers of large impacts seem to be approximately correlated with the estimated times of passage of the Sun through the galactic plane, at least for the last 65 million years. Those are predicted times for an increased near-Earth flux of comets from the Oort Cloud induced by the combined effects of galactic tidal perturbations and encounters of the Sun with passing stars. Long-term changes in the average comet flux may be related to changes in the amplitude of the z-motion of the Sun perpendicular to the galactic plane or to stripping of the outer Oort cloud by encounters with large passing stars, followed by restoration from the inner Oort cloud reservoir.