Three dualities underscore the role of repair in radiobiology: the discrete and random nature of energy deposition; the coupled processes of damage and repair; and the harmful and beneficial properties of radiation in connection with issues of public health and the radiation therapy of cancer, respectively. Starting with the survival curve of HeLa S3 cells, published by T. T. Puck and P. I. Marcus [J. Exp. Med. 103, 653-666 (1956)], the survival response of repair-competent mammalian cells is discussed and is related to clinical experience. This is followed by an examination of DNA repair in surviving cells from which it is inferred that even in repair-deficient cells, very likely large numbers of single- and double-strand DNA breaks are repaired because the progeny of surviving cells are essentially free of such damage. These observations support the idea that even when single-hit dose-effect relationships are involved (e.g., survival of ataxia telangiectasia cells), repair processes may play a role. Lastly, single-hit kinetics connected with the induction of neoplastic transformation are discussed. The data demonstrate that linear dose-response dependencies due to ionizing radiation (i.e., gamma rays and fission-spectrum neutrons) can be modulated by dose protraction, but that neither the direction nor the extent of such modulations can be predicted on theoretical grounds. To be applied more effectively for the benefit of mankind, therefore, it remains necessary to understand fully the biological mechanisms of the action of ionizing radiation.