Terrorism undoubtedly poses a grave threat to the security of open societies. Conventional wisdom holds that terrorists also hold the power to inflict serious harm to modern economies. Terrorism is a threat to security at the level of national and international frameworks as well as the entire system of world security. International terrorism is very widespread and complex, and it implies a specific form of threat that can be directed at the population, companies and above all, to the authorities. Antiterrorist policy should have a primary place in solving problems of national and international security, and should also be complex and characteristic aimed exclusively on the prevention and elimination of terrorist activities. Legislation of the state has a direct role in preventing this great problem. Terrorism has a major and significant impact on the economy of any country and affects industries such a, finance, aviation, insurance, retail, travel, tourism and transportation. Terrorism threatens international business by direct and indirect effects, and thus companies become targets of modern terrorism with important implications for operations and business performance. Terrorist incidents have economic effects by diverting foreign direct investment (FDI), demolishing infrastructure, redirecting public investment funds to security, or limiting trade. The purpose of this research is to point out contemporary terrorism, to show the influence of terrorism on the economy and modern business, and to give an overview of the new forms of action of terrorist organizations.