The paper examines topical issues of countering extremist and terrorist crimes. An analysis of terrorist activity was carried out in accordance with the available statistics for the past five years. It was noted that it is necessary to intensify preventive work to identify recruiters and accomplices of terrorists, to cut off the channels for the supply of weapons and money, to suppress the propaganda activities of radicals and extremists on the Internet. A brief forensic characteristic of extremist crimes committed using the Internet is given. Some features of the disclosure and investigation of such criminal acts are highlighted, a number of examples from the practice of the Investigative Committee of the Russian Federation are given. The types of forensic examinations that can be assigned for these categories of cases were considered, the main of which are computer (computer-technical), linguistic examinations. It is emphasized that an effective investigation of extremist crimes committed using the Internet is unthinkable without the implementation of the possibilities of using special knowledge during the investigation.