Developments in fusion power during the next decade will partially depend on the availability of advanced pumping systems. The pumping speeds required for Tokamaks with divertors may be very high, and it would be necessary for pumps to operate during the pulse as well as between pulses. Appendage pumps are not likely to be effective in cases where total speeds greatly exceed 10**6 liters/sec. For higher speeds, wall pumps surrounding the divertor target could be considered. Hydrogen experiments with near-term devices can use nonrecoverable wall pumping techniques. Wall pumps, however, will be limited to total speeds of less than similar 10**8 liters/sec. If still higher speeds are required, getter-targets may be the only options available.