High doses of ionizing radiation clearly produce deleterious consequences in humans, including, but not exclusively, cancer induction. At very low radiation doses the situation is much less clear, but the risks of low-dose radiation are of societal importance in relation to issues as varied as screening tests for cancer, the future of nuclear power, occupational radiation exposure, frequent-flyer risks, manned space exploration, and radiological terrorism. We review the difficulties involved in quantifying the risks of low-dose radiation and address two specific questions. First, what is the lowest dose of x- or gamma-radiation for which good evidence exists of increased cancer risks in humans? The epidemiological data suggest that it is approximately 10-50 mSv for an acute exposure and approximately 50-100 mSv for a protracted exposure. Second, what is the most appropriate way to extrapolate such cancer risk estimates to still lower doses? Given that it is supported by experimentally grounded, quantifiable, biophysical arguments, a linear extrapolation of cancer risks from intermediate to very low doses currently appears to be the most appropriate methodology. This linearity assumption is not necessarily the most conservative approach, and it is likely that it will result in an underestimate of some radiation-induced cancer risks and an overestimate of others.