Radiation exposures to individuals in space can greatly exceed natural radiation exposure on Earth and possibly normal occupational radiation exposures as well. Consequently, procedures limiting exposures would be necessary. Limitations were proposed by the Radiobiological Advisory Panel of the National Academy of Sciences/National Research Council in 1970. This panel recommended short-term limits to avoid deterministic effects and a single career limit (of 4 Sv) based on a doubling of the cancer risk in men aged 35 to 55. Later, when risk estimates for cancer had increased and were recognized to be age and sex dependent, the NCRP, in Report No. 98 in 1989, recommended a range of career limits based on age and sex from 1 to 4 Sv. NCRP is again in the process of revising recommendations for astronaut exposure, partly because risk estimates have increased further and partly to recognize trends in limiting radiation exposure occupationally on the ground. The result of these considerations is likely to be similar short-term limits for deterministic effects but modified career limits.