There is no proven body of fact that establishes an increase in human cancer after low doses of x or gamma radiation such as those received environmentally, occupationally, or from medical diagnostic procedures; that is, radiation levels below about 10 rad (0.1 Gy). This paper reviews the principal low dose epidemiologic studies that have investigated possible cancer increases. The results of these studies are negative, equivocal, or, when positive, invalidated by methodologic defects or by inconsistency with the feasible carcinogenic effect of background radiation. Despite the lack of direct evidence however, it will never be possible to exclude a very small cancer risk from even the lowest radiation levels, primarily because of statistical limitations in the design of epidemiologic studies. Estimates of cancer risk from low levels of x or gamma ray exposure are therefore based on assumptions regarding the relation between cancer increases and radiation dose. The statistical uncertainties of the meager human data at low doses do not permit unique relations to be established. Nevertheless recent radiobiologic investigations of dose/effect relations for neoplasms in animal populations, for chromosomal damage in human cells, and for malignant transformation in cultured mammalian cell lines suggest that a linear-quadratic relation, when fitted to the human data, provides a reasonable and conservative basis for risk estimation.