The next generation thermonuclear fusion machine ITER comprises large cryogenic pumping systems to process very high gas throughputs. The paper starts from a summary of the requirements for the torus exhaust pumping system and the neutral beam injection system for plasma heating and discusses the design solutions derived to match them. All ITER force-cooled cryopumps are based on a modular set-up and incorporate similar design of charcoal-coated cryopanels cooled to 4.5 K with supercritical helium. A systematic approach for how to design a tailor-made cryopump is presented. It is based on Monte Carlo simulation to calculate the overall capture coefficient being the primary design parameter. Experimental results measured with a model pump of representative scale are used to validate the design procedure. In the last part, the paper addresses the design issues to be solved for tritium-compatible forepumps with high pumping speeds.