The international community recognized the terrorism as one of the main modern threats to humanity. The European Union, however, still has not formed an integrated general model of interaction between the national agencies in the fight against terrorism. There is only some level of cooperation and coordination among them. By using the conventions as the main legal instrument in the fight against terrorism at the global level the international community simply reacts to the emergence of new forms and terrorist targets. Despite the fact that the conventions cover important areas of the fight against terrorism the proposals on concluding a comprehensive convention are far from realization. The negotiations on a common approach, identifying and assessing terrorism at the global level are in an impasse. The article treats different aspects of combatting terrorism and the European Union actions in this direction.