A fully understanding of the sources and characteristics of the impactors in the outer solar system is vital to obtaining a more comprehensive understanding of the impact history of the outer solar system. Owing to the huge amounts of high-quality spacecraft data, we have obtained considerable knowledge about the impact cratering processes of planetary bodies in the inner solar system. However, our understanding about the outer solar system is still extremely limited. Impactors with different size-frequency will form craters with various size-frequency distributions on icy satellites, and impactors with a range of velocity will from craters with different degree of leading-trailing (apex-antapex) hemisphere asymmetry on synchronous rotating satellites. Conversely, the size-frequency distributions and leading-trailing hemisphere distributions of impact craters on icy satellites can be used to infer the impactor sources of the outer solar system. For Jovian system, most larger craters (diameter (D)＞10~30 km) are formed from heliocentric impactors, but the degree of crater apex-antapex asymmetry observed on Ganymede and Callisto is much lower than that from theoretical estimation for ecliptic comets, which is inconsistent with current astronomical observations and theoretical computations. For Europa, most small craters (D＜1 km) are formed from secondary impactors. For Saturnian system, the distributions of larger craters (D＞20~30 km) on Rhea and Iapetus are more consistent with heliocentric impactors, while crater distributions on Mimas, Dione and Tethys are more consistent with planetocentric debris, especially for smaller craters, which are more likely to be influenced by the Saturn-orbiting impactors, such as escaped secondary ejecta from large basins and/or remnants of disrupted satellites.