The main threats to world order are terrorist and extremist activities. On the world stage, countries unite into a coalition with the aim to increase the efficiency of the fight against terrorism. At the local level, the terrorist threat is fought by the security services. In order to prevent global human victims, which may arise as a result of terrorist attacks, the government is taking a number of normative legal acts, which prevent the activities of militants. The main problem that arises in the preparation of the law is the lack of a clear understanding of what the "terrorism" and "extremism" are. Therefore, in this paper, a complete analysis of these terms will be made on the basis of normative legal acts of some countries such as the USA, Russia, Kazakhstan, and scientists specialized in the subject. Research of the terms "extremism" and "terrorism" has shown that these concepts are different, but at the same time interconnected. This relationship is expressed in the fact that terrorism is a continuation of extremism, its next step. The disengagement of these concepts will allow the legislator to create more specific laws, that will cover the entire field of criminal activities.