The impact crater flux history of the Saturnian system has been estimated based on observed crater density data from the satellite surfaces, cratering data for the terrestrial planets, and theory. The proposed cratering flux has an history similar to that for the inner solar system: an initial very high cratering rate which exponentially decayed during the first few hundred million years followed by a more constant but lower cratering rate to the present. The dominant source of crater-forming projectiles for the Saturnian satellites is suggested to be external to the Saturn system. The modeled present cratering rate at Iapertus is about the same order of magnitude as on the earth. Crater ages derived from the model suggest that most surfaces, the heavily cratered terrains, are >3.5 b.y. old. However, some surfaces have distinctly younger ages, <3.5 b.y., even considering the statistical uncertainties. The plains units on Dione and Enceladus formed over several hundred to billions of years beyond the end of the heavy bombardment.