According to various researchers, the prevalence of unruptured cerebral aneurysms (CAs) in the general population varies from 2 to 5 %. In the vast majority of cases, CAs do not have clinical and neurological manifestations and are discovered incidentally during routine neuroimaging studies. CAs can cause intracranial hemorrhage. As a rule, hemorrhages of this type occur in patients aged 40–60 years. It has been established that about 10–15 % of patients die from an aneurysmal hemorrhage before they receive specialized medical care. Recurrent aneurysmal intracranial hemorrhage is the main cause of high mortality and disability in this group of patients. The search for literature sources in the scientific databases PubMed/Medline, EMBASE, Cochrane Library and eLibrary demonstrated the existence of numerous studies devoted to the study of molecular biology and biophysical mechanisms of formation, growth and rupture of CAs. Combining the results of these studies was the motivation for writing this literature review. The paper reflects in detail the role of inflammation and molecular genetic factors in the growth and rupture of the CAs, and presents the biophysical factors of the rupture of the CAs. The authors pay special attention to the shape, size and coefficient of the CAs as the most important geometric risk factors for the formation and rupture of the CAs. This review presents current data on mathematical modeling of various types of CAs with an assessment of the risk of rupture of the latter, which has found its application in wide clinical practice. The authors also attempted to describe the hemodynamic features in various types of CAs. In turn, the type of blood flow in the CAs cavity largely depends on the size and shape of the latter and the geometry of the carrier artery, which is the basis for preoperative planning and the choice of tactics for surgical treatment of patients with unruptured CAs.