Currently, the Council of Europe plays an important role in the implementation of regional and international cooperation in the fight against terrorism. The Council of Europe has been protecting human rights, the rule of law and pluralist democracy since 1949, as well as stands for the need to combat terrorism, that denies these fundamental values. Thus, the Council of Europe is closely involved in this issue since the 1970s [3]. The Council of Europe develops legal standards to prevent and suppress acts of terrorism through criminal law and other measures, while respecting human rights and in full respect of the rule of law, and is continuously working to improve international cooperation in bringing terrorists to justice [1] . As a regional organization, the Council of Europe seeks to ensure the implementation of Resolution 1373 (2001) of the UN Security Council by providing a forum for the review and adoption of regional standards and best practices, as well as helping its member-countries to improve their ability to combat terrorism. In addition, the Council of Europe has strengthened its cooperation with other international organizations that deal with this issue, specifically with the European Union, OSCE, UN [3]. The activities of the Council of Europe on the fight against terrorism are based on three fundamental principles: reinforcement of the legal actions against terrorism; preservation of core values; carrying out of activities aimed at the elimination of the causes of terrorism [3].  Within the framework of the Council of Europe were adopted a series of international instruments against terrorism, among which are the European Convention on the Suppression of Terrorism in 1977, the Protocol on Amendments to the said Convention in 2003, Council of Europe Convention on the Prevention of Terrorism in 2005, Additional Protocol to the Council of Europe Convention on the Prevention of Terrorism in 2015, Action Plan on the fight against violent extremism and radicalization leading to terrorism in 2015. The amended Protocol to the European Convention on the Suppression of Terrorism was opened for signing on May 5, 2003. The Protocol contains a number of important amendments to the Convention:   It significantly expanded the list of offenses, which are not qualified as political or politically motivated; now it includes all the offenses specified by the UN anti-terrorism conventions;   It simplified the amendment procedure, which allows to add to that list another new violations;   The Convention was open for accession by the observer countries and other states that are not members of the Council of Europe. They can become members of the Convention after receiving the consent of the Committee of Ministers;   It provides the possibility of refusing to extradite offenders to the countries where they could face the death penalty, torture or life imprisonment without parole;   It significantly reduced the possibility of rejection of extradition on the basis of reservations of the Convention. Thus, any refusal is subject to control procedure, which also applies to all obligations, listed in the text of the amended Convention [5].  The Resolution "On Combating Terrorism", adopted at the 25th Conference of European Ministers of Justice, held on 9-10 October 2003 in the Bulgarian city of Sofia, highlights the need of strengthening the international cooperation among member states in this area.  The purpose of the Council of Europe Convention on the Prevention of Terrorism (2005) is to prevent terrorism by the signing parties and to intensify the efforts aimed at the elimination of its negative impact on the protection of human rights, particularly of the right to life. Article 4 of the Convention established the rules regarding the forms of international cooperation in the field of counter-terrorism.  The Additional Protocol to the Council of Europe Convention on the Prevention of Terrorism was meant to solve the problem of "foreign terrorist fighters" and was signed on October 22 in the Latvian capital Riga by the 18 countries. The Additional Protocol is designed for early prevention of terrorism, and includes the restriction of foreign terrorist flows to such countries as Syria and Iraq, qualifying participation in a terrorist group, or travel abroad for terrorist purposes, as well as the preparation, organization and funding of travel for this purpose as a criminal offense [4]. The Action Plan on the fight against violent extremism and radicalization leading to terrorism has two objectives: to reinforce the legal framework against terrorism and violent extremism; to prevent and fight violent radicalization through concrete measures in the public sector, in particular in schools and prisons, and on the Internet [2]. Also, it should be noted that there are several specialized structures in the Council of Europe that carry out the fight against terrorism. Among them are the Committee of Experts on Terrorism (CODEXTER), the Committee on Foreign Terrorist Fighters and Related Issues (COD – CTE).  Committee of Experts of The on Terrorism (CODEXTER) follows the implementation part of the Council of Europe legal-Instruments Against Terrorism and coordinates the Council of Europe activities Insider in Combating Terrorism. For 2016-2017, CODEXTER established three priorities: Terrorism and the Internet; Links between terrorism and organised crime; Assessment of possible gaps in the legal framework provided by Council of Europe international legal instruments in the area of the prevention and suppression of terrorism, including with respect to International Humanitarian Law and terrorism and also in relation to the absence of a common definition of “terrorism” in International Law [1]. The Committee on Foreign Terrorist Fighters and Related Issues (COD-CTE) was established on 21 January 2015 by the Committee of Ministers of the Council of Europe to prepare a draft Additional Protocol supplementing the Council of Europe Convention on the Prevention of Terrorism (CETS No. 196). The COD-CTE, composed of experts from all Member and Observer States of the Council of Europe, as well as from other relevant international organisations, and working under the authority of the CODEXTER, is mandated to examine the criminalisation of the following acts: being recruited for terrorism; receiving training for terrorism; traveling to another state for the purpose of the perpetration or preparation of terrorist acts; providing or collecting funds for such travels; organising and facilitating such travels. The efforts of the Council of Europe are aimed at strengthening legal measures against terrorism and are based on the principle that it is possible and necessary to fight against terrorism, while supporting the human rights, fundamental freedoms and the rule of law.  Today the European Community cannot feel satisfied by the efforts made in the fight against international terrorism. The main thing that is required in order to stop the growth of terrorism is the unification of the whole European community against terrorist ideology to deprive terrorism of its ideological reasons and to reduce its social base. This should be a main priority in the future activities of the Council of Europe.