After decades of research on low-Earth orbit, national space agencies and private entrepreneurs are investing in exploration of the Solar system. The main health risk for human space exploration is late toxicity caused by exposure to cosmic rays. On Earth, the exposure of radiation workers is regulated by dose limits and mitigated by shielding and reducing exposure times. For space travel, different international space agencies adopt different limits, recently modified as reviewed in this paper. Shielding and reduced transit time are currently the only practical solutions to maintain acceptable risks in deep space missions.