The United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR) assesses the levels and effects of exposure to ionizing radiation. UNSCEAR’s scientific findings underpin radiation risk evaluation and international protection standards. This report comprises a report to the General Assembly with two underpinning scientific annexes. The first annex recapitulates and clarifies the philosophy of science as well as the scientific knowledge for attributing observed health effects in individuals and populations to radiation exposure, and distinguishes between that and inferring risk to individuals and populations from an exposure. The second annex reviews the latest thinking and approaches to quantifying the uncertainties in assessments of risk from radiation exposure, and illustrates these approaches with application to examples that are highly pertinent to radiation protection. The report is a landmark publication in terms of our understanding of the confidence that can be attached to the attribution of health effects in individuals and populations, and to the estimation of risks inferred from exposure to ionizing radiation.