The terrorist attacks on the World Trade Center and the Pentagon were not only the most audacious and successful terrorist attacks the world has yet seen, but also marked the maturation of what had been described as the 'new terrorism'. There had been voices in the national security community, including on the National Security Council itself, warning about transnational threats such as terrorism and organised crime. If the potential for Atlantic divisions remained very considerable, however, the common interests of the United States and its European allies in combating the challenge from radical Islamic terrorism are difficult to overestimate. This chapter provides a conceptual analysis and assessment of terrorist threats. It considers the nature of the responses that are required as both the United States and European governments adapt to what is a very different kind of security challenge from that for which they prepared during the Cold War.