Before the human exploration of Mars or long-duration missions on the Earth's moon, the risk of cancer and other diseases from space radiation must be accurately estimated and mitigated. Space radiation, comprised of energetic protons and heavy nuclei, has been shown to produce distinct biological damage compared with radiation on Earth, leading to large uncertainties in the projection of cancer and other health risks, and obscuring evaluation of the effectiveness of possible countermeasures. Here, we describe how research in cancer radiobiology can support human missions to Mars and other planets.