This article addresses issues relevant to interpreting findings from 26 epidemiologic studies of persons exposed to low-dose radiation. We review the extensive data from both epidemiologic studies of persons exposed at moderate or high doses and from radiobiology that together have firmly established radiation as carcinogenic. We then discuss the use of the linear relative risk model that has been used to describe data from both low- and moderate- or high-dose studies. We consider the effects of dose measurement errors; these can reduce statistical power and lead to underestimation of risks but are very unlikely to bring about a spurious dose response. We estimate statistical power for the low-dose studies under the assumption that true risks of radiation-related cancers are those expected from studies of Japanese atomic bomb survivors. Finally, we discuss the interpretation of confidence intervals and statistical tests and the applicability of the Bradford Hill principles for a causal relationship.