Abstract
This article discusses the scientific research of terrorism and extremism carried out by scientists from Kazakhstan, Russia and some other countries. A variety of approaches and methods used by experts are studied. The theoretical and practical importance of scientific papers dealing with terrorism and extremism is shown. The authors pay particular attention to the conceptual study of terrorism and extremism. It is noted that the concepts of terrorism and extremism are sometimes confused and equaled not only in the general social, but also in scientific ideas. Research conducted by the authors revealed the absence of clear wording of terrorism and extremism, the mixing of these concepts in scientific works and in the criminal law in different countries. In this regard, the authors justify the need for a clear separation of the concepts of terrorism and extremism in the criminal law to uniquely qualify these crimes.