Recent years have seen a series of large-scale terrorist attacks, which are often interpreted as a new kind of threat in the 21st century: globalised and indiscriminate violence inspired by violent extremist ideologies derived from Islam and directed against the West. This interpretation challenges the concept of a rules-based international community and could, ultimately, undermine Europe’s relations with its southern neighbours. This Paper provides an overview of global terrorism today, in particular the al-Qa‘ida phenomenon. Its origins, history, development from local organisations to a global network, the role of migration, the main elements of its ideology as well as its moral ambiguities (and potential weaknesses) are discussed. It is argued that global terrorism is not the expression of an ideological confrontation between Islam and the West, but that it reflects political problems that have not been addressed, from lack of economic development and bad governance, over unresolved conflicts and violence, to historical insensitivities towards the specificities of Muslim societies. The responsibility lies with both Arab governments and the West. In order to address these issues, Europe should be willing to act autonomously from the US and exploit the main weakness of al-Qa‘ida and similar organisations, which is their totalitarian, intolerant and arbitrary character.