In classical theories of radiobiological action, cell killing is viewed as an inevitable consequence of the accumulation of some given number of physical "hits" in sensitive, intracellular targets. Shoulders on survival curves are attributed to the need for more than one hit to produce the observed effect, and to the random distribution of these hits among the cells in an irradiated population. Such curves start with zero slope at very low doses, and, at high doses, they approach, asymptotically, exponential slopes that are inversely proportional to the dose required for one hit, or to inactivate a single target. Unfortunately, these simple ideas provide no credible explanation for the dramatic changes in apparent final slope, and the total abolition of shoulders, that are observed in many radiation-sensitive mutants. The damage-repair hypothesis asserts that the surviving fraction of cells in a mutagen-treated population is proportional to the number of potentially lethal lesions that are not removed by any repair process. Evidence indicates that these repairable lesions are located in DNA; however, this fact is irrelevant to the mathematical development of dose-response equations under the damage-repair hypothesis. The survival curves for repair-proficient cells generally exhibit a shoulder which reflects a decline in the efficiency of repair with increasing dose. Introduction of the concepts of "error-prone" and "recombinagenic" repair allows the extension of these ideas to data on induced mutation and mitotic recombination.