Introduction: NanOx is a theoretical framework developed to predict cell survival to ionizing radiation in the context of radiotherapy. Based on statistical physics, NanOx takes the stochastic nature of radiation at different spatial scales fully into account. It extends concepts from microdosimetry to nanodosimetry, and considers as well the primary oxidative stress. This article presents in detail the general formalism behind NanOx. Methods: Cell death induction in NanOx is modeled through two types of biological events: the local lethal events, modeled by the inactivation of nanometric sensitive targets, and the global events, represented by the toxic accumulation of oxidative stress and sublethal lesions. The model is structured into general premises and postulates, the theoretical bases compliant with radiation physics and chemistry, and into simplifications and approximations, which are required for its practical implementation. Results: Calculations performed with NanOx showed that the energy deposited in the penumbra of ion tracks may be neglected for the low-energy ions encountered in some radiotherapy techniques, such as targeted radionuclide therapy. On the other hand, the hydroxyl radical concentration induced by ions was shown to be larger for low-LET ions and to decrease faster with time compared to photons. Starting from the general formalism of the NanOx model, an expression was derived for the cell survival to local lethal events in the track-segment approximation. Discussion: The NanOx model combines premises of existing biophysical models with fully innovative features to consider the stochastic effects of radiation at all levels in order to estimate cell survival and the relative biological effectiveness of ions. The details about the NanOx model formalism given in this paper allow anyone to implement the model and modify it by introducing different approximations and simplifications to improve it, or even adapt it to other medical applications.