[en] Biologically based risk projection models for radiation carcinogenesis seek to describe the fundamental biological processes involved in neoplastic transformation of somatic cells into malignant cancer cells. A validated biologically based model, whose parameters have a direct biological interpretation, can also be used to extrapolate cancer risks to different exposure conditions with some confidence. In this article, biologically based models for radiation carcinogenesis, including the two-stage clonal expansion (TSCE) model and its extensions, are reviewed. The biological and mathematical bases for such models are described, and the implications of key model parameters for cancer risk assessment examined. Specific applications of versions of the TSCE model to important epidemiologic datasets are discussed, including the Colorado uranium miners' cohort; a cohort of Chinese tin miners; the lifespan cohort of atomic bomb survivors in Hiroshima and Nagasaki; and a cohort of over 200,000 workers included in the National Dose Registry (NDR) of Canada. (author)