Radiation exposure leads to a large number of victims who seek medical help in the first hours. To provide medical care, it is necessary to correctly establish the fact and dose of radiation by bioindication and biodosimetry methods. Lymphocytes containing nuclear anomalies are easily detected cells of peripheral blood and are suitable as objects of bioindication in the case of radioactive exposure to a large number of people. Among these anomalies we distinguish micronuclei, "tailed" nuclei, nucleoplasmatic bridges, dumbbell-shaped nuclei, etc. This review observes the main types of these nuclear anomalies of lymphocytes in the light of their common origin from dicentric chromosomes. We recommend using these alterations in peripheral blood lymphocytes nuclei as the simplest biomarkers in the framework of bioindication tests when it is necessary to work with a large number of victims.