In connection with the events taking place in the world the past few years, the issue of national and public security has become one of the most urgent and priority. The first two decades of the XXI century are filled with violence, where the greatest importance is the threat of extremism and terrorist activities which gaining momentum every year. Although extremism and terrorism are an odious phenomena they are not related to a specific social group, which has a special world view, and often they are defined as a form of violence used to achieve certain goals, the main problem of existence of data phenomena is opposition of the Western world to the world of radical Islam. At the moment, the global community is undergoing a number of changes, there is a reassessment of values, axiological world view based on belief in progress, humanism and liberalism is broken on an unprecedented flowering of violent forms of struggle for defending and approval of alien to the European cultural tradition ideology. Manifestations of extremism and terrorism, the escalation of the conflict that pervades all aspects of society, shows the destructive nature of cultural processes taking place in modern society. The article deals with the concept of cross-cultural interaction, analyzes the features of its manifestation in the modern world. The author considers the phenomenon of violence, forms of its manifestation, focuses on terrorism, as an element of culture and as an extreme form of violence.