This report gives an introductory overview of what the current research has so far been able to document about anti-democratic and violence-promoting environments in Denmark that subscribe to Islamist ideologies. It does not map or give a complete description of such environments in Denmark, as the present body of research is far from adequate for this. Instead, the report is an attempt to gather existing knowledge and identify its results and limitations, so as to provide a basis for future work. As the report is concerned with both anti-democratic and violence-promoting environments in Denmark that subscribe to Islamist ideologies, it sets out by establishing a conceptual framework that distinguishes between the many different ways in which it is possible to act on the basis of a given set of views. Distinctions are made between private and public actions, between political and apolitical, between democratic, anti-democratic and violence-promoting actions, and finally between legal and illegal actions.