Over the last 40 years the amount of knowledge about human radiation effects has increased dramatically. During that interval, radiation epidemiologists have documented a number of additional types of radiation-induced cancer and have established rough estimates of the magnitude of cancer risks. Nevertheless, we currently have inadequate knowledge about a number of factors that help define the magnitude of radiation risks. These include questions of estimating risk over the lifetime, shapes of dose-effect curves, magnitude of risks at low doses, potentiation between radiation and other agents, and the nature and role of host susceptibility factors. Data from various studies are used to illustrate these questions.