The discovery of heavily cratered surfaces on Ganymede and Callisto by Voyager 1 shows that like the inner Solar System a period of heavy bombardment also occurred in the outer Solar System. Comparisons among the crater size/density curves of Ganymede, Callisto and the terrestrial planets show several striking features. The overall crater density of the most heavily crated terrain on the Ganymede is down by a factor of about 3 compared to Callisto, and when allowance is made for the difference in crater production rate due to the influence of Jupiter's gravity field it is down by a factor of nearly 6. This indicates that the oldest regions of Ganymede began recording the observed crater population at a later time than Callisto, and therfore Ganymede either experienced a large-scale (perhaps global diameter independent resurfacing event or simply developed a rigid crust capable of retaining craters later than Callisto. In either case, this process took place during the period of late heavy bombardment. Based on earlier studies of the terrestrial-planets' cratering record, neither Ganymede nor Callisto is saturated with craters. Compared to Callisto, a diameter-dependent loss of craters in the size range 10--40 km occures on the grooved terrain of Ganymede and probably results from obliteration of small craters due to the formation of new ice. A similar but less severe loss also occurs on Ganymede's heavily cratered terrain and may be due to an earlier period of ice formation and/or the formation of arcuate troughs in this terrain. Seven different crater curves, in the diameter range of about 40--130 km, representing vastly different crater densities, different surface ages, different terrain types, and even different satellites all possess nearly the same distribution function. This together with other observational evidence strongly suggests that at least in this diameter range the curve basically represents its production function which is completely different from that on the terrestial planets. This indicates that the population of bodies responsible for the period of late heavy bombardment in the inner Solar System was very different from that responsible for the late bombardment in the outer Solar System. We can only speculate at this early stage that Ganymede and Callisto may principally record a population of bodies that never penetrated the inner Solar System in numbers great enough to leave a recongnizable signature.