medical Academy of Postgraduate Education, ministry of Health of the Russian Federation, moscow, RussiaThe paper presents basic radiobiological models in radiation oncology as the theories that predict the effect in normal tissues and in tumors during their ionizing radiation. It shows their mathematical basis leaning upon an event in a certain cell, as well as they are applied to the practice of radiation therapy to calculate the dose of radiation and the number of fractions per treatment cycle in order to adjust the dose sufficient for tumor destruction, by preserving the viability or physiological function of normal tissues and organs. The paper considers how the radiobiological models allow one to compare the biological effect of irradiation in a variety of dose adjustment over time, i.e. during different fractionation modes and how they are used to represent physical quantities (e.g. an absorbed dose) as clinical indicators, such as a biologically effective dose, tumor control probability, and normal tissue complication probability, which are used to optimize radiation plans. It gives the history of radiobiological models and the current view on their role in the practice of radiotherapy.