Our understanding of the molecular and cellular response to ionizing radiation (IR) has progressed considerably. This is notably the case for the repair and signaling of DNA double-strand breaks (DSB) that, if unrepaired, can result in cell lethality, or if misrepaired, can cause cancer. However, through the different protocols, techniques, and cellular models used during the last four decades, the DSB repair kinetics and the relationship between cellular radiosensitivity and unrepaired DSB has varied drastically, moving from all-or-none phenomena to very complex mechanistic models. To date, personalized medicine has required a reliable evaluation of the IR-induced risks that have become a medical, scientific, and societal issue. However, the molecular bases of the individual response to IR are still unclear: there is a gap between the moderate radiosensitivity frequently observed in clinic but poorly investigated in the publications and the hyper-radiosensitivity of rare but well-characterized genetic diseases frequently cited in the mechanistic models. This paper makes a comprehensive review of semantic issues, correlations between cellular radiosensitivity and unrepaired DSB, shapes of DSB repair curves, and DSB repair biomarkers in order to propose a new vision of the individual response to IR that would be more coherent with clinical reality.