This article is the attempt of complex analysis of terrorism as an international and national problem of the day. For a long time, terrorism was considered as a problem of internal security of individual country, but its scale clearly proved the limitation of this approach It focuses onthe characteristics of international terrorism, defined by their relevance to Ukraine. Also investigated researches and developments for combating terrorism in the context of international and national security, identified the need for effective prevention, response and counter terrorist threats to the lives and health of Ukrainian citizens. Formulated definition of the concept of terrorism as a socio-political phenomenon that aims at the use (or threatened use) of violence among the citizens of a state for the sake of destabilization or loosening of the political system.2. Specify the grounds in which terrorism, in our opinion, recognized by the international. Given the characteristic features of international terrorism. Shows the ranking of countries for terrorist offences in 2015.Given the statistical data of the General Prosecutor of Ukraine on the fact of Commission of terrorist crimes in the period from 2013–2016, on the number of persons convicted of terrorist offences in the period from 2013 – 01.07.2016.
Keywords: terrorism, terrorist act, challenges, risks, punishment