The article is devoted to the consideration of such a phenomenon as modern terrorism and the problem of its classification. For today, domestic and foreign scientists and practicians have proposed numerous options for classifying terrorism, some of which will be considered in this study. In particular, an analysis of the classifications of terrorism will be carried out, proposed by doctors of law, professors V.V. Luneev, Yu.M. Antonyan and S.U. Dikaev, doctor of philosophy V.V. Kaftan and other Russian scientists, as well as a representative of foreign science - the American psychologist J. Post. In the explored types of classifications, the most successful and universal ones were allotted, as well as those that are due to their novelty and non-standard approach of interest. At the same time, a number of disadvantages were identified not to let to recognize many classifications as universal and appropriate to the norms of criminal law. The article also pays special attention to the mistakes made by members of the public and the mass media, highlighting such types of terrorism that do not take place either in reality or in the theory of legal science. Based on the analysis of existing classifications, the authors proposed the most acceptable options from the point of view of the science of criminal law and criminology, accounting the trends of modern terrorism.