Research into genetic and physiological mechanisms of widespread disorders such as arterial hypertension as well as neuropsychiatric and other human diseases is urgently needed in academic and practical medicine and in the field of biology. Nevertheless, such studies have many limitations and pose difficulties that can be overcome by using animal models. To date, for the purposes of creating animal models of human pathologies, several approaches have been used: pharmacological/chemical intervention; surgical procedures; genetic technologies for creating transgenic animals, knockouts, or knockdowns; and breeding. Although some of these approaches are good for certain research aims, they have many drawbacks, the greatest being a strong perturbation (in a biological system) that, along with the expected effect, exerts side effects in the study. Therefore, for investigating the pathogenesis of a disease, models obtained using genetic selection for a target trait are of high value as this approach allows for the creation of a model with a “natural” manifestation of the pathology. In this review, three rat models are described: ISIAH rats (arterial hypertension), GC rats (catatonia), and PM rats (audiogenic epilepsy), which are developed by breeding in the Laboratory of Evolutionary Genetics at the Institute of Cytology and Genetics (the Siberian Branch of the Russian Academy of Sciences).